The depiction appeared towards the end of the video, asserting debunked claims that the 2020 election - which he lost to Joe Biden - was stolen from him.
Posted on Mr Trump's own social media network, the two-second clip shows the Obamas as apes bobbing up and down to the tune of The Lion Sleeps Tonight.
The post was later deleted - around 12 hours after being shared.
A White House official said a member of staff "erroneously made the post" and it had now been taken down.
Later, while onboard Air Force One, the US president said that "of course" he condemned the racist parts of the video, but told journalists he would not apologise, and did not say whether he would fire the staffer who posted it.
"No, I didn't make a mistake," he said, adding that he didn't see the full video. "I looked at the beginning of it. It was fine."
He then said: "I looked in the first part and it was really about voter fraud in, and the machines, how crooked it is, how disgusting it is.
"Then I gave it to the people. Generally, they'd look at the whole thing. But I guess somebody didn't, and they posted. We took it down as soon as we found out about it."
'Every single Republican must denounce this'
The post sparked widespread outrage from across the political spectrum, while the White House's response was also criticised.
Kamala Harris, Mr Trump's Democratic rival in the 2024 presidential election, said: "No one believes this cover-up from the White House, especially since they originally defended the post.
"We are all clear-eyed about who Donald Trump is and what he believes."
In a message on X, formerly Twitter, Gavin Newsom, the Democratic governor of California, accused the president of "disgusting behaviour" over the post.
He added: "Every single Republican must denounce this. Now."
Responding to the video, Senate Democratic leader Chuck Schumer wrote on X: "Racist. Vile. Abhorrent. This is dangerous and degrades our country-where are Senate Republicans?"
Mr Schumer urged the US president to apologise to the Obamas, calling the couple "two great Americans who make Donald Trump look like a small, envious man".
Ben Rhodes, who served as deputy national security adviser in the Obama White House, reacted to the video by calling Mr Trump "a stain on our history".
"Let it haunt Trump and his racist followers that future Americans will embrace the Obamas as beloved figures while studying him as a stain on our history," he wrote on X.
George Conway - ex-husband of Kellyanne Conway, who managed the president's successful election campaign in 2016 - responded by highlighting an article he'd written describing Mr Trump as a "racist" in 2019.
The group Republicans Against Trump wrote: "There's no bottom."
White House initially criticised 'fake outrage'
Before the post was removed, White House press secretary Karoline Leavitt defended it and said the depiction formed part of a longer video depicting various politicians as animals.
She said: "This is from an internet meme video depicting President Trump as the King of the Jungle and Democrats as characters from The Lion King.
"Please stop the fake outrage and report on something today that actually matters to the American public."
Mr Trump has a long history of attacking Mr Obama, his predecessor as president, and was a vocal proponent of the "birther" conspiracy theory.
The theory cast doubt on Mr Obama's birth in Hawaii, asserting that he was actually born in Kenya, and therefore ineligible to hold the office of president.
Mr Obama produced his long-form birth certificate in 2011. In 2016, Mr Trump publicly accepted that his predecessor was born in the US.
Pleas from International Olympic Committee (IOC) president Kirsty Coventry to be respectful were ignored when four Israelis entered the San Siro in the athlete parade.
You had to listen carefully, but boos could be heard over the music in the vast stadium.
Simultaneous parades were held at Games clusters across northern Italy - while jeering was reported in Predazzo, there were cheers when Israelis marched in the mountain resort of Cortina d'Ampezzo.
Israel has endured more harrowing days at the Olympics, with 11 of their athletes murdered by Palestinian terrorists in a massacre at Munich in 1972.
For these Olympics, the IOC faced pressure to ban Israel from competing over the thousands killed in the post-7 October war in Gaza, but rejected those calls.
The jeering demonstrated the animosity of some in the crowd towards the Jewish state, with hostility over conflict and geopolitical tensions hard to escape in the ceremony.
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Fractures between Europe and the United States were also evident.
While American athletes entered to cheers, the brief appearance of vice president JD Vance, waving Stars and Stripes flags with wife, Usha, did prompt more booing and whistling.
Anger against the Trump administration has been evident in the buildup to the Games, with protests against Immigration and Customs Enforcement agents being here to protect the US delegation, weeks after their personnel killed two American citizens.
But if you were watching on television, you probably didn't hear the booing - drowned out by music or commentators.
Italians will have revelled in hearing Mariah Carey paying homage to the hosts by singing iconic 1950s hit Volare in Italian.
Maybe you did hear the cheers for Ukraine, a show of solidarity four years into the full-scale invasion by Russia, whose team remains banned.
There were enthusiastic roars, too, for Venezuela following Trump's military interventions.
The IOC wanted to show a world uniting through sport, hoping these Games are a platform for compassion to shine rather than conflict.
"You'll show us that strength isn't just about winning," Ms Coventry told athletes in her address. "It's about courage, empathy and heart."
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It is about a vast Olympics. For the next two weeks, five sporting clusters across northern Italy will be in the sporting spotlight.
An Olympic Games has never been as sprawling across such a large footprint. It is an even wider platform-to-platform.
But Ms Coventry told her first opening ceremony leading the Olympics that "when we see rivals embrace at the finish line, we are reminded that we can choose respect".
Boxes were seen being carried from his property in Camden, north London, on Friday evening, while police cars were parked in the driveway of Mandelson's Wiltshire house.
Plain-clothed officers also used torches to briefly search a Range Rover outside the London address.
Latest updates on Mandelson investigation
Metropolitan Police deputy assistant commissioner Hayley Sewart said the "central specialist crime team" were carrying out the warrants.
"The searches are related to an ongoing investigation into misconduct in public office offences, involving a 72-year-old man," said a statement.
"He has not been arrested and enquiries are ongoing."
The search is part of an investigation into Lord Mandelson following the latest release of files about paedophile financier Jeffrey Epstein, which have revealed more details about the pair's relationship.
They appear to show Mandelson passed on market-sensitive information to Epstein when he was business secretary after the 2008 financial crisis.
Lord Mandelson has denied any wrongdoing in relation to Epstein. He has said he regrets maintaining a relationship with him and apologised to the sex offender's victims.
'Significant volume of material' to be reviewed
Sir Keir Starmer remains under pressure to release documents related to the peer's vetting to become UK ambassador to the US - a job he was sacked from in September.
The prime minister has said Mandelson lied about the depth of his friendship with Epstein ahead of getting the prestigious Washington job.
In a letter to the chair of parliament's Intelligence and Security Committee (ISC), Sir Keir said he wanted the documents released as soon as possible.
However, he said "a very significant volume of material" on Mandelson's appointment as ambassador needed to be reviewed first.
In Friday's letter, Sir Keir said he had told the cabinet secretary to work with the ISC on "how material that may be prejudicial to the UK's national security and international relations is shared and reviewed".
Documents coming 'shortly'
Speaking to journalists earlier, Downing Street said the government would publish the documents "shortly".
Sky News understands the government is working with police to ensure any document released does not undermine the police investigation into Mandelson.
Officials are believed to be in the early stages of assessing the documents, of which there are thousands.
The scandal surrounding Lord Mandelson has left Sir Keir under severe pressure, with some in Labour wanting him to resign.
Labour MPs are urging Sir Keir to reveal whether he saw a report by an influential party peer that warned of Lord Mandelson's links to Epstein.
Labour grandee Lord Glasman told Sky News last September that he had flagged to Number 10 about the pair's relationship but was met with a "discreet suggestion to basically shut up".
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In an interview with Sky News' Sophy Ridge, Lord Glasman suggested he was asked to report to Number 10 about the pair's relationship and he did - but suggested no action was taken.
"They asked me to send a report and I sent a report," he said.
"I did say when I got back, I would think again about this publicly.
"Then I did get a discreet suggestion to basically shut up about that, and I did."
McSweeney under pressure
Even more focus has been placed on the prime minister's chief of staff, Morgan McSweeney, who was a close political ally of Lord Mandelson.
Labour backbencher MP Simon Opher called for a "clear out at Number 10".
"If my chief of staff had done this, I think he would be looking for another job," Mr Opher told the BBC.
Veteran Labour MP Clive Efford and Southport MP Patrick Hurley have also said Mr McSweeney should leave Number 10.
PM's future
Former cabinet minister and Labour grandee Harriet Harman told the Electoral Dysfunction podcast previously that the prime minister needed a "real reset".
Sir Keir could lose his premiership if he does not do the right thing, Ms Harman added.
However, so far no big names on the current frontline of Labour politics have turned their fire on the prime minister and his staff.
Sir Keir on Thursday apologised for believing Lord Mandelson's "lies" about his closeness to Epstein.
The prime minister made Lord Mandelson the UK's ambassador to the US in 2024.
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Following a partial release of the Epstein files last year, Sir Keir sacked him after it emerged how close the pair were.
Another tranche of millions of documents released by the US government recently saw Mandelson quit Labour and resign from the House of Lords.
Nancy Guthrie, the daughter of NBC's Today show co-host Savannah Guthrie, is feared to have been kidnapped.
The 84-year-old was last seen at her own home near Tucson, Arizona, on the evening of Saturday 31 January, with a local TV station since receiving two messages that appear to be connected to the case.
One demanded money in exchange for her return and contained information about her Apple watch and floodlights on her property.
On Friday, a spokesperson for the convenience store chain Circle K told NBC News, Sky News's US partner, that officers visited one of their stores after "receiving a tip regarding a vehicle of interest, and our team has provided them access to the store's surveillance video".
Officials have not said whether the vehicle or vehicles are connected to any part of the disappearance.
It comes as the FBI and Pima County Sheriff's Department said they were aware of a "new message regarding Nancy Guthrie".
It was not clear what the message was or if it was connected to previously reported notes.
The message was sent to Tucson TV station KOLD, three officials briefed on the meeting told NBC News.
The FBI is working to confirm if it came from the same sender as the first reported ransom note, the sources said.
They stressed that the FBI has not yet verified if the first note came from someone who may have taken Ms Guthrie from her home.
Ms Guthrie's children have released two videos appealing to her apparent kidnappers.
On Wednesday, Savannah Guthrie posted a video in which she tearfully pleaded for her mother's safe return and appealed to the presumed kidnappers to open a line of communication with the family.
On Thursday evening, her son Cameron Guthrie said in a video posted to his sister's Instagram account: "Whoever is out there holding our mother, we want to hear from you."
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US President Donald Trump, speaking to reporters on Air Force One, said late on Friday that the investigation into Ms Guthrie's disappearance was going "very well".
"We have some clues that I think are very strong," he added. "We have some things that may be coming out reasonably soon."
US attorney general Pam Bondi told reporters earlier on Friday that federal authorities were assisting Arizona officials, but she declined to offer details.
"It breaks my heart for Savannah and for her family," she added.
Meanwhile, the sheriff investigating Ms Guthrie's disappearance said concern about her condition is growing because authorities say she needs daily medicine.
Pima County Sheriff Chris Nanos said: "Her conditions, I would imagine, are worsening day by day.
"She requires medication. And I have no way of knowing whether they're getting that medication to her."
Ms Guthrie was said to have a pacemaker and dealt with high blood pressure and heart issues, according to the sheriff's dispatcher audio on broadcastify.com.
Dyfed-Powys Police said the boy has been remanded in custody and is scheduled to appear at Swansea Magistrates' Court on Saturday.
Officers were called to Milford Haven Comprehensive School in Pembrokeshire, southwest Wales, at about 3.20pm on Thursday, following a report that a teacher was assaulted by a pupil brandishing a weapon.
Police said the teacher was taken to hospital for treatment and later discharged.
All of the pupils "returned home unharmed" on Thursday, the force said, adding that the school was closed on Friday.
Detective Chief Inspector Matthew Briggs, senior investigating officer, said the force is "continuing to support the victim whilst they recover from this traumatic event".
He said the injuries suffered by the victim "have now been confirmed as stab wounds", and "there will continue to be a higher than usual police presence in the area over the coming days to provide further reassurance".
Police officers will also be "working closely with local secondary schools to offer support over the coming week", he added.
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Welsh First Minister Baroness Eluned Morgan, who had visited the school last week, said on Thursday evening that she was "deeply concerned by the incident".
"My thoughts are with the injured teacher, their family and the entire school community during this difficult time," she added.
"I want to pay tribute to the emergency services and school staff for their swift and professional response in ensuring the safety of pupils and staff.
"While this remains an active police investigation that must be allowed to proceed without interference, I want to be unequivocal... violence of any kind has no place in our schools."
The first minister also said the Welsh government will "continue to work closely with local authorities, schools and partners to support all those affected and to ensure our schools remain safe environments for learning and care".




