Britain's largest police force has been placed on heightened alert for any rise in hate crime following the referendum result.
Mayor of London Sadiq Khan said he had asked Scotland Yard to be "extra vigilant" after a number of incidents were reported in the capital and around Britain.
It came as the Poland's ambassador expressed shock at incidents of "xenophobic abuse" directed 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 1.5 million 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."
Scotland Yard commissioner Sir Bernard Hogan-Howe described London as a "diverse, global city where people from many different backgrounds live and work side-by-side in safety".
He added: "That hasn't changed in the past few days but if people do have any concerns they should let the police know. We will investigate vigorously any reports of crime motivated by hatred. "
The Mayor said he was proud of London's "famed and well-deserved reputation" for diversity.
He said: "Many people from all over the world live and work here, contributing to every aspect of life in our city. I say to them all, you are, and you will continue to be, welcome in London and in all our communities."
Police are investigating vandalism at a Polish community building in London after images on social media appeared to show graffiti in which the words "F*** you OMP" were smeared in yellow paint across the entrance, before it was cleared.
Officers are probing the criminal damage at the Polish Social and Cultural Association (POSK), in Hammersmith, west London.
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 on Monday: "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.
"At the same time, we would like to thank for all the messages of support and solidarity with the Polish community expressed by the British public. We call on all Polish nationals who fall victim of xenophobic abuse and on all witnesses to report such incidents to local authorities."
Other incidents were also reported on social media and a hashtag of #PostRefRacism was being used on Twitter.
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."
Another user, James Titcombe, said: "Daughter tells me someone wrote '[Child's name] go back to Romania' on the wall in the girls toilets at School today."
Immigration was a central theme in the build-up to the referendum.The Leave camp has stressed that there would be no change for EU citizens already living in the UK.