"President Trump got the message from the many Londoners who love and admire America and Americans but find his policies and action the polar opposite of our city's values", Khan said in a statement released on Twitter.
Downing Street said no date has been confirmed for any visit by Mr Trump and that the opening of the U.S. embassy "is a matter for the US".
He blamed Barack Obama's administration for a "bad deal" despite the fact the move was agreed under George W Bush.
In his tweet Mr Trump said: "Reason I cancelled my trip to London is that I am not a big fan of the Obama Administration having sold perhaps the best located and finest embassy in London for "peanuts", only to build a new one in an off location for 1.2 billion dollars". In an outburst on Twitter, the U.S. president said the new location is "bad" and no, he won't cut the ribbon.
The current ambassador, Robert "Woody" Johnson, said the change was necessary even though the US had been linked to Grosvenor Square for more than 200 years.
Trump has not ruled out a visit to the British capital in the future. The idea had gradually evolved into a working visit in which Trump would open the London embassy. In December, USAmbassador to Panama John Feeley resigned in protest of Trump's policies, ahead of the president deriding Latin American nations such as Haiti and El Salvador as "s***hole countries", Reuters reported Friday.
In Washington, White House spokeswoman Sarah Huckabee Sanders said Trump's comment was exclusively about an embassy-related visit.
Trump's roiling of diplomatic relations caused disruptions in the Western Hemisphere as well.
But British officials have been dismayed by some of Trump's pronouncements, particularly a proposed ban on Muslims entering the United States and most recently when Trump rebuked May on Twitter after she criticised him for retweeting British far-right anti-Islam videos.
Labor party lawmaker David Lammy said that the bombastic billionaire was unnerved by the possibility of being "met by millions of us out on the streets protesting".
The British government said the opening of the embassy was a matter for the United States.
Last month Labour leader Jeremy Corbyn called for his supporters to go out in force to send Mr Trump a "clear message" that he is not welcome if he comes to the UK.
Some British lawmakers questioned whether Trump would be welcome in London because of previous tweets and criticism of Muslims and his sniping at London Mayor Sadiq Khan in the aftermath of a terror attack in that city a year ago.
But British Foreign Secretary Boris Johnson suggested the decision was prompted by the opposition to Trump in Britain, and warned such critics "seem determined to put this crucial relationship at risk".