Mayor of London Sadiq Khan asked Scotland Yard to be “extra vigilant” after a flurry of incidents were reported in the capital and around Britain.
It came as Poland’s ambassador to the UK expressed shock at “xenophobic abuse” against the Polish community.
Mr Khan said: “I take seriously my responsibility to defend London’s fantastic mix of diversity and tolerance.
“So it’s really important we stand guard against any rise in hate crimes or abuse by those who might use last week’s referendum as cover to seek to divide us.
“I’ve asked our police to be extra vigilant for any rise in cases of hate crime, and I’m calling on all Londoners to pull together and rally behind this great city.”
Addressing hate crimes will be a priority for the Metropolitan Police, he said, adding: “We will have a zero-tolerance approach to any attempt to hurt and divide our communities.
“It’s also crucial that we don’t demonise the 1.5m people in London who voted for Brexit.
“While I and millions of others disagreed with their decision, they took it for a variety of reasons and this shouldn’t be used to accuse them of being xenophobic or racist. We must respect their decision and work together now to get the best deal for London,” he said.
David Cameron also condemned incidents of abuse and hatred directed at migrants.
The prime minister told a special meeting of Cabinet in 10 Downing Street that his government would not “tolerate intolerance” against nationals of other EU states.
Police are investigating vandalism at a Polish community building in London after images on social media appeared to show graffiti in which the words “Fuck you” were smeared in yellow paint across the entrance, before it was cleared.
Cambridgeshire Police are investigating suspected post-referendum racism after notes were allegedly posted through letterboxes of Polish residents in the county.
Laminated cards reading “Leave the EU — no more Polish vermin” were reportedly delivered to members of the Polish community in Huntingdon, north-west of Cambridge, on Saturday.
Polish ambassador to Britain Witold Sobkow said: “We are shocked and deeply concerned by the recent incidents of xenophobic abuse directed against the Polish community and other UK residents of migrant heritage.
“The Polish embassy is in contact with relevant institutions, and local police are already investigating the two most widely reported cases in Hammersmith, London, and Huntingdon, Cambridgeshire.
Sky News journalist Adam Boulton tweeted: “This weekend I and my family have witnessed 3 “when are you going home?” racist incidents aimed at EU citizens here.”