Rishi Sunak has said that planned protests on Armistice Day would be "provocative and disrespectful".
There is a risk war memorials such as the Cenotaph in London could be "desecrated", the prime minister added.
Organisers of next week's march have insisted they have no plans to be near the Cenotaph on 11 November.
Chief Rabbi Sir Ephraim Mirvis said the line between protesters supporting innocent Palestinians and backing Hamas have become "badly blurred".
Writing in the Times, he said: "Those lines have remained blurred in the subsequent demonstrations, in which a minority have proudly displayed their extremism on their banners and in their chants, while the majority stand alongside them".
The Met Police is planning a "significant" operation and has been in contact with organisers, who said they were "willing to avoid the Whitehall area", where the war memorial is located.
Pro-Palestinian protests have been held in London, and other cities globally, each Saturday since the Israel-Gaza war began.
Mr Sunak said on Friday: "To plan protests on Armistice Day is provocative and disrespectful, and there is a clear and present risk that the Cenotaph and other war memorials could be desecrated, something that would be an affront to the British public and the values we stand for."
He has also written a letter to Met Police chief Sir Mark Rowley, saying the force has the government's "full support in making robust use of all your powers to protect Remembrance activity".
He added he was "deeply concerned that a number of protests are currently planned to disrupt" acts of remembrance.
Sir Mark responded by saying police "recognise the profound importance of remembrance events" and are committed to ensuring they "take place without disruption".
Mr Sunak has asked Home Secretary Suella Braverman to support the police in "doing everything necessary to protect the sanctity of Armistice Day and Remembrance Sunday".
Ms Braverman said there was an "obvious risk of serious public disorder, violence and damage" if the protest on 11 November went ahead, describing it as a "hate march through London".
Several events to mark the end of World War One are typically held across the UK on Armistice Day, which is always on 11 November.
This year these include a two-minute silence commemorating the war dead, and the daytime and evening Festival of Remembrance at the Royal Albert Hall in London, with the latter performance usually attended by members of the Royal Family.
On Remembrance Sunday, which this year falls on 12 November, thousands of servicemen and women usually march past the Cenotaph war memorial in central London, where military veterans are joined by senior politicians and members of the Royal Family.
The 11 November protest is expected to call for a ceasefire on the Gaza Strip.
Organisers said they were aware of the importance of the date, and their previous demonstrations had been peaceful and orderly.
Ben Jamal, director of Palestine Solidarity Campaign, said it had "made clear that we have no intention of marching anywhere near Whitehall out of respect for events taking place at the Cenotaph".
He added the march will begin almost two hours after the silence of commemoration for the war dead.
"Each of the protests we have called have been peaceful, orderly, and attended by hundreds of thousands of demonstrators from a diverse cross section of British society," he said, adding that "to suggest that undertaking protests well away from Whitehall is a disrespect for the war dead is an insult to those marching for peace".
Responding to Mr Sunak's comment about "disrespectful" protests, Yasmine Ahmed, UK director of the international campaign group Human Rights Watch, called them "cynical, culture-war politics and an attack on our democratic freedoms".
The Met said a "significant policing and security operation" would be conducted on 11 and 12 November, and that it was "absolutely committed to ensuring the safety and security of anyone attending commemorative events".
"We will use all the powers available to us to ensure anyone intent on disrupting it will not succeed," a spokesperson said.
They added that the police were aware of a "significant demonstration" planned for 11 November, but not Remembrance Sunday, and that organisers were "engaging with our officers and have said they are willing to avoid the Whitehall area, recognising the sensitivities around the date".
On Friday, five people were arrested during a pro-Palestinian sit-in at London's King's Cross station after the demonstration was banned. Transport Secretary Mark Harper said he had given an order to allow police to stop the protest.
More on Israel-Gaza war
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History behind the story: The Israel-Palestinian conflict
Israel has been bombarding Gaza with prolonged air strikes following the 7 October attacks on southern Israel by Hamas, in which they killed 1,400 people and took more than 200 hostage.
The Hamas-run health ministry in Gaza says Israeli air strikes have killed more than 9,000 people.
Hamas is a proscribed terrorist organisation in the UK.
Protests in London have been largely peaceful, although there have been 99 arrests of people who attended the three massive weekly marches in London.
BBC reporters who have witnessed the demonstrations have seen a wide range of people from different backgrounds attending, including lots of families with children.
On Friday, two women were charged with a terror offence after allegedly carrying "an image displaying a paraglider" at a pro-Palestinian protest in London, and police are still looking for a third woman.
Mayor of London Sadiq Khan said it was "incredibly important" that demonstrators understood the importance of Remembrance events, telling PA News: "I'd encourage the organisers to work with the police to stay away from the Cenotaph."
It comes as Met commissioner Sir Mark told the London Assembly that he was "deeply concerned" about the impact on community policing after 3,500 officers were redeployed to central London protests in the past three weeks.
The Campaign Against Antisemitism has also written an open letter to Sir Mark, after he said hate crime laws "probably need redrawing" as he faced questions about the policing of pro-Palestinian marches.
The letter, signed by lawyers, said it is "quite clearly the case that there are existing laws that are simply not being applied or enforced with sufficient rigour" by the Met.
Ahead of planned protests this coming weekend, the Met said there would be a "sharper focus" on potential criminal behaviour, and would be using facial recognition technology to identify known suspects, including potential terrorists.
Scotland Yard also said that since 1 October it has received 554 crime reports of antisemitic incidents - in the same period last year the police investigated 44 such reports.
The number of reported Islamophobic hate crimes for the same period has reached 220 - up from 70 during the same period last year.
So far 133 people have been arrested. Of those, 26 have so far been charged - 14 in relation to alleged antisemitism and six for alleged Islamophobia.