She criticised what she called "lies" linking her to the late sex offender in a surprise address filmed in the Grand Foyer of the White House.
The First Lady said the claims were "defaming her reputation".
"The lies linking me with the disgraceful Jeffrey Epstein need to end today," she said.
"I am not Epstein's victim," she added. She also called for a congressional hearing for survivors.
Mrs Trump also said she had never had a relationship with Epstein's associate Ghislaine Maxwell, with whom she said she had only a casual correspondence.
Epstein was found dead in his Manhattan cell in 2019, aged 66, facing sex trafficking charges.
Mrs Trump added: "I have never been friends with Epstein. Donald and I were invited to the same parties as Epstein from time to time, since overlapping social circles is common in New York City.
"To be clear, I never had a relationship with Epstein or his accomplice, Maxwell."
It is understood many of Mrs Trump's staffers gathered to watch the statement but that several of them did not know what she was going to say.
A reporter from MS Now posted on X that Mr Trump told the outlet he did not "know anything about" the First Lady's statement.
'Absolutely extraordinary'
Sky News' US correspondent Mark Stone called the address "absolutely extraordinary".
He said: "I can't think of a precedent for a First Lady making such a statement like this ever before.
"We knew she was going to make a statement but we had no idea what it would be about, and it was about an elephant that has been in the room for quite some time.
"There have been rumours that have been circulating for quite some time about an alleged relationship or acquaintance between Mrs Trump and Epstein. She has decided to get out ahead of those, and ahead of perhaps more that may come out.
"Some of what she has said and the tone in which she has said it suggests perhaps that she was getting ahead of stories that may yet emerge.
"And she wanted to make quite clear she had absolutely no relationship with Epstein, she said 'I am not Epstein's victim'."
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Asked why she may have chosen this moment, Stone added: "It's a good question, and I don't know, but the tone in which she was speaking and the fact that she says numerous fake images had been circulating, then said 'be cautious about what you believe, these stories are completely false', there is perhaps some concern within the White House, within the administration, that more emails are due to emerge, which the White House believes may look as though they are implicating Mrs Trump."
Mrs Trump's statement in full
"Good afternoon. The lies linking me with the disgraceful Jeffrey Epstein need to end today. The individuals lying about me are devoid of ethical standards, humility and respect.
"I do not object to their ignorance, but rather, I reject their mean-spirited attempts to defame my reputation.
"I have never been friends with Epstein. Donald and I were invited to the same parties as Epstein from time to time, since overlapping in social circles is common in New York City and Palm Beach. To be clear, I never had a relationship with Epstein or his accomplice Maxwell.
"My email reply to Maxwell cannot be categorised as anything more than casual correspondence. My polite reply to her email doesn't amount to anything more than a trivial note. I am not Epstein's victim.
"Epstein did not introduce me to Donald Trump. I met my husband by chance at a New York City party in 1998. This initial encounter with my husband is documented in detail in my book Melania.
"The first time I crossed paths with Epstein was in the year 2000 at an event Donald and I attended together. At the time, I had never met Epstein and had no knowledge of his criminal undertakings.
"Numerous fake images and statements about Epstein and me have been circulating on social media for years now. Be cautious about what you believe.
"These images and stories are completely false. I'm not a witness or a named witness in connection with any of Epstein's crimes. My name has never appeared in court documents, the depositions, victim statements or FBI in interviews surrounding the Epstein matter.
"I have never had any knowledge of Epstein's abuse of his victims. I was never involved in any capacity. I was not a participant, was never on Epstein's plane and never visited his private island.
"I have never been legally accused or convicted of a crime in connection with Epstein, sex trafficking, abuse of minors and other repulsive behaviour.
"The false sneers about me from mean spirited and politically motivated individuals and entities looking to cause damage to my good name to gain financially and climb politically, must stop.
"My attorneys and I have fought these unfound and baseless lies with success, and will continue to maintain my sound reputation without hesitation.
"To date, several individuals and companies have been legally obligated to publicly apologise and retract their lies about me, such as Daily Beast, James Carville and HarperCollins UK.
"Now is the time for Congress to act. Epstein was not alone. Several prominent male executives resigned from their powerful positions after this matter became widely politicised.
"Of course, this doesn't amount to guilt, but we still must work openly and transparently to uncover the truth.
"I call on Congress to provide the women who have been victimised by Epstein with a public hearing specifically centred around the survivors.
"Give these victims their opportunity to testify under oath in front of Congress with the power of sworn testimony.
"Each and every woman should have her day to tell her story in public, if she wishes, and then her testimony should be permanently entered into the Congressional Record. Then, and only then, we will have the truth. Thank you."
Two of Epstein's accusers, Maria and Annie Farmer, said in response to the comments: "What we want is accountability, transparency and justice."
John Healey said a Russian Akula-class attack submarine and two specialist submarines from Russia's main directorate for deep sea research (GUGI) were directed by president Vladimir Putin to "conduct hybrid warfare activities against the UK and our allies, specifically around critical undersea infrastructure".
He said they were detected within the UK's exclusive economic zone, which stretches around 230 miles offshore.
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The attack submarine was a "likely decoy" to divert attention away from the other two, he added.
Mr Healey, speaking at a conference in Downing Street, said he directed the British military to track the vessels, by sea and air, in a month-long mission with allies to prevent attacks on cables and pipelines.
A Royal Navy frigate, HMS St Albans, were used in the operation along with RFA Tidespring. Merlin helicopters and RAF Boeing "submarine hunting" aircraft also tracked the Russian vessels.
The operation involved working with the Norwegian military.
Moscow has rejected claims the ships pose a threat to the UK's critical underwater infrastructure, Russian news agency TASS reported.
GUGI is thought to have access to more than 50 ships, submarines and other vessels, including the Yantar, a Russian spy ship spotted in British waters in November, which allegedly used lasers to dazzle RAF pilots.
'We see you'
Mr Healey said: "I'm making this statement to call out this Russian activity.
"To President Putin, I say - we see you, we see your activity over our cables and our pipelines, and you should know that any attempt to damage them will not be tolerated and will have serious consequences."
He then said the UK's undersea network was highly resilient but that the number of threats to it are increasing, adding: "Putin's covert operation failed because this government is delivering our first duty - protecting Britain."
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The operation used more than 500 British personnel and has now ended, he added.
He also said there was "no evidence" that the Russian submarines have caused any damage to UK underwater cables or pipelines.
Distracted by the Middle East
But he claimed it was "pretty clear" that Putin wants the UK to be distracted by the war in the Middle East, in response to a question from Sky News' security and defence editor, Deborah Haynes.
He said: "I'm pretty clear that Putin would want us to be distracted by the Middle East.
"What I'm setting out today demonstrates that we are not just exposing his covert operation, but we are saying to him that we recognise Russia as the primary threat to the UK and to NATO, and that we will not take our eyes off Putin, whilst at the same time we act to protect our British interests and our British allies in the Middle East."
Defence spending
Asked by Ms Haynes if he believes the UK's defence spending needs to be pushed towards 3% faster, he said: "I would just say to you, look back at the speeches that the chancellor has made. She has quite rightly argued a strong economy needs strong national security.
"Look back at the £8bn we're now spending each year on defence, above the level of the last government's last year in office."
The slump in popularity of a country that is meant to be the other half of Britain's special relationship also came after the US intervention in Venezuela.
Consultancy company Public First found that 53% of Britons questioned said they regarded the US as a "negative force in the world" - a jump of 19 percentage points since before American forces seized Venezuelan President Nicolas Maduro in January.
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By contrast, just 29% of respondents viewed Washington as a positive force - a drop of 12 percentage points compared with last December.
The figures were gathered for the two-day London Defence Conference, which opens on Friday.
Conference director Iain Martin said: "The British public has dramatically shifted in attitudes towards the US after the war in Iran".
"That represents a profound challenge to the transatlantic alliance with potentially serious implications for the special relationship.
"These poll numbers emphasise the need to strengthen British and allied defences in the face of growing threats and global instability."
The survey, which quizzed just over 2,000 adults in the UK, found that an overwhelming majority - 85% - believed that the world was becoming more dangerous, with 60% saying it felt the most unstable in their lifetime.
Mr Trump's foreign policy was widely seen as escalating risk, with 64% of respondents saying that his approach makes a global conflict more likely.
On the war in Iran, just 26% were in favour of the US and Israeli military action, while 41% were against.
Roughly half (49%) of the public thought Sir Keir Starmer's involvement in the crisis was broadly correct, with 48% saying he should refuse to offer help if asked directly by Washington.
However, that ratio would change if Iran were to hit British military targets in the region.
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Should that happen, 59% of those asked said they would support UK involvement.
As for unblocking the Strait of Hormuz to tanker traffic, if the UK had the best chance of reopening oil trade in the region, some 47% of Britons said the military should be deployed compared with 31% who preferred that it stays away.
With wariness about the United States growing, the poll found a growth in support for greater European cooperation. This included 38% of people saying they would prioritise strengthening ties with European countries, compared with just 19% favouring the US.
Sky News is the official media partner of the London Defence Conference 2026. Later this year Sky News will launch a new defence & security app, bringing together video-first reporting from our leading journalists and experts.
Armed police were called to Hardale Grove, Dormanstown, Redcar, shortly after 1.30pm on Thursday following concerns for a child.
The child died after they arrived at the property, the force said.
Cleveland Police believe the child died as a result of a dog bite.
Armed officers attended and one dog was destroyed on the street, while another at the property was recovered by police.
The North East Ambulance Service said three crews were sent and one person was taken to hospital for further treatment.
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Emily Harrison, district commander for Redcar and Cleveland, said: "Understandably this is a distressing and tragic incident, and our thoughts are with the child's family.
"There is a scene in place at the address while an investigation into the child's death begins.
"I would encourage anyone who has concerns or information to please speak to an officer."
Carlo Tritta, from Eastleigh, Hampshire, had pleaded guilty to offences including making indecent images of a child, engaging in sexual communications with a child, and intimidating a witness.
He was 18 when he began messaging his victim on the gaming app, building her trust online until she felt they were in a relationship.
After moving to other platforms as well as Roblox, he then encouraged her to send explicit sexual images.
Soon, the grooming moved offline and Tritta started sending the girl - whose identity is protected by law - gifts and takeaways at her family home.
After a year of grooming, the victim's mother became concerned and reported Tritta to the police.
"I can't even explain how I felt, what I'd seen on my girl's phone," the victim's mother told Sky News.
"I can't even explain it, it's like... I have medication to calm me down, I'm in therapy.
"It's like a continuing nightmare," she said.
After his arrest, when he was ordered not to contact the girl, he continued to do so.
Tritta, now 19, sent his victim greeting cards containing his new phone number, because his old phone was being held by the police, and contacted her friends.
In one card, he warned her if the case against him ended up in court, "both our names" would be "ran through dirt for the world to see".
He also warned her the officer leading the case was male and "would see anything", and claimed he had tried to stop that.
Tritta travelled from his Hampshire home to her home in Manchester several times and maliciously called social services about the girl's mother, as well as telling the teenager he had called the police on her mother and brother "for your protection".
In December, he was arrested for perverting the course of justice after he tried to get his victim to drop the charges. But, three days after he was given a suspended sentence, Tritta returned to her family home.
He was rearrested and was charged with a series of child sex offences.
In court the next day, Tritta pleaded guilty to three counts of making indecent images of a child, engaging in sexual communications with a child, causing a child aged 13-15 to watch/look at a sexual image, two counts of intimidating a witness, and criminal damage.
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"Once the police came, and they sat talking to my daughter, and they asked, 'Where did you meet him?' [She said] 'Roblox'. I was like... 'Roblox? The kids game you go on? What?'" said the victim's mother.
She blames Roblox for what happened to her daughter, because she said the company "should do more" to protect children.
"[It's] a child's game where predators are going on. And they might not even be necessarily there to groom children but they can talk to them freely and do what they want," she said.
"It's like a nice playing field for them with children, isn't it?"
A Roblox spokesperson said: "We are deeply saddened to hear of this troubling case. With more than 144 million daily active users on Roblox, cases of harm are rare, but we know any incident of harm is one too many and we are committed to building safeguards designed to prevent that from happening."
They added: "We cannot comment on this specific case but we work closely with law enforcement to support investigations and will take action where violations of our Terms of Service are found."