After United States President Donald Trump cancelled his planned visit to London, Mayor Sadiq Khan on Friday said that the former "got the message" from Londoners.
Many British politicians have voiced their opposition to Trump being granted a state visit, and say the invite should be recalled.
Mr Trump also criticised the location of the new building in Vauxhall, south London, as an "off location", adding: "Wanted me to cut ribbon-NO!"
Trump said in a late-night tweet that he had decided not to come to London to open the new USA embassy.
The US embassy move was confirmed in October 2008, when President George W Bush was still in the White House.
Mrs May controversially extended the offer of a state visit, officially on behalf of the Queen, when she became the first world leader to meet Mr Trump in the White House following his inauguration previous year.
Many Londoners have made it clear that Donald Trump is not welcome here while he is pursuing such a divisive agenda.
"The US is the biggest single investor in the United Kingdom - yet Khan & Corbyn seem determined to put this crucial relationship at risk", Johnson said in a tweet.
He said Trump's visit "would without doubt have been met by mass peaceful protests".
A Number 10 source said: "Boris expresses himself in his own inimitable way, but we agree that any risk to the crucial US-UK relationship is not in our country's best interests". "We will not allow US-UK relations to be endangered by some puffed up pompous popinjay in City Hall".
A spokesman for May's Downing Street office said the invitation for the state visit "has been extended and accepted".
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"The US is one of our oldest and most valued allies and our strong and deep partnership will endure", the spokesman said.
Almost two million British people added their names to an online petition in 2017 calling for Trump's visit to be downgraded from a state visit to avoid embarrassing the queen.
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.
There had always been security concerns about the Grosvenor Square site, dating back to the late 1990s after attacks on USA embassies in Africa.
He conceded that the former building in upmarket Mayfair, central London, was a "perfect location" but noted it was viewed as too vulnerable following the September 11, 2001, attacks.
The area became known as "Little America" at the time.
The new building will open for business on January 16.
"A multi-disciplinary team of professionals considered over 170 criteria, to include physical security requirements, and determined that the Nine Elms site was the best overall location for the USA government".
However, the opponents threatening of mass protests on Trump enters the country, is being cited as a major reason behind the cancellation of the latter's plan.
Bemused construction workers and passers-by took selfies with the Trump waxwork, which was first unveiled at Madame Tussauds in January past year.