Police have asked organisers to consider postponing any protests in central London this Armistice weekend.
However one of the groups planning a pro-Palestinian march on Saturday has said it is "determined to go ahead".
The prime minister has condemned the plan to march on Armistice Day- when people pause at 11am to remember the war dead - as "provocative and disrespectful".
Rishi Sunak said there was "a clear and present risk" that memorials such as the Cenotaph "could be desecrated".
Home Secretary Suella Braverman called it "entirely unacceptable to desecrate Armistice Day with a hate march through London".
Organisers have said the protest will avoid the Cenotaph, instead going from Hyde Park to the American embassy, and that it won't start until well after the 11am silence.
But the Met's Assistant Commissioner Ade Adelekan said "the risk of violence and disorder linked to breakaway groups is growing".
"This is of concern ahead of a significant and busy weekend in the capital," he added.
"Our message to organisers is clear: Please, we ask you to urgently reconsider. It is not appropriate to hold any protests in London this weekend."
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A pro-Palestinian protest in central London on 28 October
Stop The War coalition said it had met police on Monday and "argued that we wanted to march and were determined to go ahead".
"We believe that this is a denial of our civil liberties and our freedom of expression," it said.
"The brutal onslaught on Gaza is being protested across the world. We have had huge demos on Palestine and we continue to do so.
"The Tory government and right wing media all oppose a ceasefire and they want to silence those who represent the majority in calling for one."
Thousands have protested in London in recent weeks over Palestinian deaths in the Israel-Hamas war, with 11 arrests during a fourth week of protests last Saturday, when a dispersal order was authorised.
Five people were also arrested at a pro-Palestinian protest at King's Cross station on Friday.
No demonstrations are planned for Remembrance Sunday, when veterans parade past the Cenotaph and politicians and royals lay wreaths.
Police have said "all powers and tactics" are available, including asking the home secretary to ban Saturday's march under the Public Order Act if there's a risk of serious disorder.
"We fully appreciate the national significance of Armistice Day," said Met Commander Karen Findlay.
"Thousands of officers will be deployed in an extensive security operation and we will use all powers and tactics at our disposal to ensure that anyone intent on disrupting it will not succeed."
Scottish First Minister Humza Yousaf - whose family was trapped in Gaza until recently - has said the march on Armistice Day should go ahead - and said he was livid at the language used by the UK government.
"Yes, in every single march, I'm afraid you'll get one or two idiots who will do and say something that we all universally condemn," he said.
"But to describe those hundreds of thousands in London, in cities across the UK, including here in Scotland, as full of hate or hate marches is completely unacceptable."