London and Manchester police have called for protests to be delayed or cancelled after the synagogue terror attack.
Metropolitan Police said it wanted to deploy every available officer to protect Jewish communities, but was instead having to prepare for a protest against the banning of Palestine Action.
Politics latest: Mahmood says pro-Palestinian protests 'dishonourable' after Manchester attack
The Met said it was "having to plan for a gathering of more than 1,000 people in Trafalgar Square on Saturday in support of a terrorist organisation".
It added: "By choosing to encourage mass law breaking on this scale, Defend Our Juries [the protest organisers] are drawing resources away from the communities of London at a time when they are needed most."
Palestine Action was banned under anti-terrorism laws in July.
Greater Manchester's police chief echoed the call, urging protest organisers in the city to ask "whether this is really the right time".
"You could do the responsible and sensitive thing and refrain, on this occasion, from protesting in a manner which is likely to add to the trauma currently being experienced by our Jewish community," said Chief Constable Sir Stephen Watson.
He said peaceful gatherings would not be stopped but warned officers would "act immediately to curtail any acts of violence, intimidation or threat".
Defend Our Juries, which has led demonstrations against the Palestine Action ban, said it planned to go ahead with the march.
"Today, the Metropolitan Police wrote to us to ask that we postpone Saturday's mass protest in Trafalgar Square, citing 'significant pressure on policing'," said a statement.
"Our response in short: Don't arrest us then."
It comes after the home secretary criticised separate pro-Palestinian protests held last night as "fundamentally un-British" and "dishonourable".
A demonstration - held to protest the Israeli navy halting a flotilla carrying aid to Gaza - was held in London's Whitehall on Thursday evening, hours after the attack in Crumpsall in which two men were killed.
The Metropolitan Police said 40 people had been arrested in the course of the protest, six of whom were arrested for assaults on police officers.
Speaking to Anna Jones on Sky News Breakfast, Shabana Mahmood said she was "very disappointed" to see the protests go ahead, given the context.
"I think that behaviour is fundamentally un-British," she said. "I think it's dishonourable."
She said the issues that had been driving the pro-Palestine protests have been "going on for some time" and "don't look like they're going to come to an end any day soon" - but that those behind the demonstrations could have taken a "step back".
"They could have stepped back and just given a community that has suffered deep loss just a day or two to process what has happened and to carry on with the grieving process," she said.
"I think some humanity could have been shown."
Any further protests must "comply with the law and, where someone steps outside of the law of our land, they will be arrested", the home secretary warned.
She added: "And to anybody who is thinking about going on a protest, what I would say is, imagine if that was you that has had a family member murdered on the holiest day in your faith. Imagine how you would feel and then just step back for a minute, give people a chance to grieve.
"We can get back to our protests later - just because you have a freedom doesn't mean you have to use it."
However, Zack Polanski, the leader of the Green Party, accused the home secretary of being "deeply irresponsible" for her comments about pro-Palestine protests.
"I think ultimately conflating protests against the genocide in Gaza and ultimately weaponising that against an anti-Semitic attack on our streets, a terrorist attack, is deeply irresponsible," he told Sky News Breakfast.
The Green Party leader said it was "worrying when governments are increasingly trying to crush down dissent" and using "what is a brutal attack... to try and make a point about protest".
"We need statesmanship at this moment. We need responsibility," he added.
The two men killed outside the Heaton Park Hebrew Congregation Synagogue in Thursday's attack have been named by police as Adrian Daulby, 53, and Melvin Cravitz, 66.
The suspect has been named as Jihad al Shamie - a 35-year-old British citizen of Syrian descent.
He is understood to have been granted British citizenship in 2006 when he was around 16 years old, having entered the UK as a young child.
Ms Mahmood confirmed to Sky News that the perpetrator was not known to counter-terror police and that he had not been referred to the government's anti-terrorism scheme Prevent.
Three other people - two men in their 30s and a woman in her 60s - have been arrested on suspicion of the commission, preparation and instigation of acts of terrorism.
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Asked if she was concerned about further attacks, Ms Mahmood said the government was on "high alert".
She said there had been an increase in police resources not just in Manchester but across he country.
"We as a government want to make sure that people feel safe going about their business today; so people will see an increased police presence, particularly around synagogues and other places of interest for the Jewish community," she said.
(c) Sky News 2025: Police call for protest against Palestine Action ban to be cancelled after Manches