The action has been taken after the activist group claimed responsibility for breaking into RAF Brize Norton last week.
Footage released online by Palestine Action showed two people inside the Oxfordshire military base.
The clip showed one riding an electric scooter up to an Airbus Voyager air-to-air refuelling tanker and appearing to spray paint into its jet engine - with reports of damage totalling millions of pounds.
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Home Secretary Yvette Cooper said "the disgraceful attack on Brize Norton" on Friday was "the latest in a long history of unacceptable criminal damage committed by Palestine Action".
She said a draft proscription order will be laid in parliament next week and if passed, it will make it illegal to be a member of, or invite support for, Palestine Action.
Proscription can lead to prison sentences of up to 14 years for some offences, although some breaches are punishable with fines.
Read more: What does proscription mean?
Saeed Taji Farouky, a member of the group, told Sky News the proscription was "completely irrational" and "without precedent".
He branded it a "knee-jerk reaction from the government" because the group "was able to humiliate them and show serious flaws in the defences of the RAF base".
Armed forces minister Luke Pollard said a "full review" of security at military bases was under way, and the government was working alongside counter-terror police to find the activists who broke into the Oxfordshire base.
The group has also claimed responsibility for several incidents involving red paint being sprayed on businesses.
Read more:
Who are Palestine Action?
Barclays targeted by activists
A protest in support of Palestine Action took place on Monday in London.
Sir Mark Rowley, the head of the Metropolitan Police, said he was "shocked and frustrated" that the action was going ahead.
The Metropolitan Police said 13 people were arrested at the protest in Trafalgar Square - six for assaulting an emergency worker and one person for a "racially aggravated public order offence".
Four people were arrested for breaching Public Order Act conditions after refusing to disperse following the imposed 3pm cut-off, and two more were held for obstructing a constable in the execution of their duty.
A Met spokesperson said officers at the protest were "surrounded on each occasion they tried to deal with an incident".
In her statement to parliament, Ms Cooper said Palestine Action "publicises and promotes its attacks involving serious property damage".
She said the group had claimed responsibility for an attack on a Jewish-owned business in north London, as well as causing millions of pounds of damage to defence businesses.
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The home secretary said, however, that if parliament supports the proscription, the right to "peaceful protest" will remain unaffected.
"It is vitally important that those seeking to protest peacefully, including pro-Palestinian groups, those opposing the actions of the Israeli government, and those demanding changes in the UK's foreign policy, can continue to do so," she added.
Tzipi Hotovely was challenged on the deaths of innocent civilians by Wilfred Frost after two British surgeons, who have worked in Gaza during the Israeli bombardment, filmed video blogs for Sky News.
He asked how many children it is "legitimate and proportionate" to kill, including those being treated in hospital, in order to kill Hamas terrorists.
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Ms Hotovely said Israel was "not there to kill anyone" and "never targets civilians", with its attacks complying with international law.
Dr Victoria Rose, a consultant plastic surgeon, who has worked in Gaza hospitals for three separate periods, previously told Sky she felt the number of children coming through the doors was "barbaric".
She said there were "more innocent children, let alone adults, that are dying per Hamas scalp that you see".
Asked about her account, Ms Hotovely said: "We never targeted the children, it's Hamas that needs to be blamed…But they need to blame Hamas for creating this reality for the Palestinian people."
She added: "For every life lost in Gaza, you need to blame Hamas for committing the crimes on 7 October and for committing the war crimes by using people as human shields."
Hamas-led militants killed some 1,200 people, mostly civilians, and abducted 251 people in the October 7 2023 attack.
The group is still holding 50 hostages, with less than half of them believed to be alive.
Israel's retaliatory offensive has killed more than 55,000 Palestinians, according to the Hamas-run health ministry in Gaza, which has said women and children make up more than half of the dead. It does not distinguish between civilians and combatants.
Ms Hotovely said Israel is "not interested in wars", adding: "So we are asking a very simple request from the international community - pressure Hamas to release our hostages and we will have a better condition to get to a ceasefire."
The announcement comes after Health Secretary Wes Streeting met families who have lost babies and amid the ongoing investigations at some NHS trusts into maternity care failings.
The investigation in England is intended to provide truth to families suffering harm, as well as driving urgent improvements to care and safety, as part of efforts to ensure "no parent or baby is ever let down again".
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The Royal College of Midwives (RCM) welcomed the government's announcement and said maternity services were "at, or even beyond, breaking point".
Last week, the NHS regulator said maternity and neonatal services at two Leeds hospitals had been rated inadequate over safety issues.
Mr Streeting, who was speaking at the Royal College of Obstetricians and Gynaecologists (RCOG) conference in London, apologised on behalf of the NHS for what families had been through and said it was "clear something is going wrong".
He added: "For the past year, I have been meeting bereaved families from across the country who have lost babies or suffered serious harm during what should have been the most joyful time in their lives.
"What they have experienced is devastating - deeply painful stories of trauma, loss, and a lack of basic compassion - caused by failures in NHS maternity care that should never have happened.
"Their bravery in speaking out has made it clear: we must act - and we must act now."
Mr Streeting said families have had to "fight for truth and justice" and had described being "ignored, gaslit, lied to, manipulated and damaged further by the inability for a trust to simply be honest with them that something has gone wrong".
The investigation will consist of two parts.
The first will investigate up to 10 of the most concerning maternity and neonatal units, including Sussex, in the coming weeks to give affected families answers as quickly as possible, according to the Department of Health.
The second will be a "system-wide" look at maternity and neonatal care, uniting lessons from past inquiries to create one clear set of actions designed to improve NHS care.
A National Maternity and Neonatal Taskforce will be chaired by Mr Streeting and made up of experts and bereaved families.
The investigation will begin this summer and report back by December.
Sir Jim Mackey, chief executive of NHS England, said: "This rapid national investigation must mark a line in the sand for maternity care - setting out one set of clear actions for NHS leaders to ensure high quality care for all."
Dr Ranee Thakar, president of the RCOG, said: "The maternity workforce is on its knees, with many now leaving the profession."
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RCM chief executive Gill Walton said: "Everyone involved in maternity services - the midwifery community, obstetricians, anaesthetists, sonographers and, of course, the women and families in their care - knows that maternity services are at, or even beyond, breaking point.
"This renewed focus and commitment by the health secretary to deliver change is welcome, and we will do everything we can to support him in doing so."
The fire started on Sunday in three separate locations near the main town, which is also called Chios. The flames were fanned by strong winds and turned into one large blaze.
Local media footage and photos showed firefighters battling towering flames burning through woodland and farmland as night fell. Power cuts have also been reported.
Greek authorities sent fresh evacuation notifications for two areas near Chios town on Monday morning.
Push alerts have been sent to mobile phones in the area urging people to evacuate a total of 16 villages, settlements and neighbourhoods on the outskirts of the town.
"The situation remains critical as firefighting forces are still dealing with many active fronts, several of which being near hamlets," a Greek government spokesman said.
The fire department said 190 firefighters were trying to control the fire on Monday, with strong winds hampering their efforts.
Some 35 vehicles, five helicopters and two water-dropping planes were also involved in the effort.
A specialist fire department arson investigation team has been sent to the eastern Aegean island to look into the causes.
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Wildfires are common during Greece's hot, dry summers but authorities have said climate change is fuelling bigger and more frequent blazes.
Last year, hundreds of tourists and residents were forced to flee wildfires on the holiday island of Kos.
In 2023, forest fires killed at least 20 people in the north of the country and forced 19,000 people to flee the island of Rhodes.
The 67-year-old announced his diagnosis on social media, saying it was one of stage four "advanced" cancer.
He said he was "fortunate to have a simply outstanding medical team" looking after him that was "administering the best possible care with expertise, compassion and sensitivity".
"I'm responding positively to their excellent treatment, and feeling well," he added.
"I'm blessed to be fortified by the monumental love and support of my wife, family and close friends.
"Needless to say, my message to all men over 50, in high risk groups, or displaying symptoms, is get yourself tested and campaign for routine prostate screening by the NHS.
"Early detection is crucial. And be aware, this disease can sometimes progress rapidly without obvious symptoms."
Murnaghan said he would be taking part in Sir Chris Hoy's charity bike ride in Glasgow in September, which aims to "shine a spotlight" on stage four cancer.
Sir Chris was himself diagnosed with stage four prostate cancer in September 2023.
Advanced prostate cancer is when the cancer cells have spread to other parts of the body, according to Macmillan Cancer Support.
Murnaghan is a familiar face to Sky News viewers as one of its main presenters from 2007 until 2023.
In September 2022, he announced the death of the late Queen Elizabeth II on the channel.
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Before joining Sky, he presented ITV's News At Ten and the BBC Ten O'Clock News - now known as BBC News At Ten - as well as Channel 4 News.
Murnaghan also presented quiz show Eggheads on BBC Two for 11 years.