Johnson, a Trump appointee, also said the new embassy was entirely paid for by the sale of other London properties and "did not cost the US taxpayer a cent".
Prime Minister Theresa May invited Trump for a state visit when she met with him at the White House soon after he took office previous year.
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!" But Foreign Secretary Boris Johnson blamed Khan and Labour Party leader Jeremy Corbyn for discouraging the US leader from coming. The move, which ended a 200-year USA association with London's Grosvenor Square, was part of American efforts to secure diplomatic staff in compounds - a push tied to terror concerns after al-Qaida bombings at two US embassies in East Africa a decade ago.
He said it was due to concerns about the embassy's move from the elite Mayfair district to a less fashionable area of London.
Simon Dawson Reuters
There had been speculation that the trip would be merged with a planned state visit to Britain offered to Trump by Prime Minister Theresa May, which has met with strong public and political opposition.
"His visit ... would without doubt have been met by mass peaceful protests", Khan said.
"It seems he's finally got that message".
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".
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"We are still working with our United Kingdom allies to find a date for a visit for the invitation that was offered and accepted, " she said Friday. "We will not allow US-UK relations to be endangered by some puffed up pompous popinjay in City Hall".
The "strong and deep" partnership between Britain and the United States "will endure" despite Mr Trump's cancellation, a spokesman added.
It makes it even harder to finalise the state visit that he was afforded so graciously by the Queen a year ago. Last month, Ambassador Woody Johnson, who was appointed by Trump, called it a "bargain".
On Friday night, a spokesman for the US embassy said: "The US chancery in Grosvenor Square had aged beyond its ability to be improved to current security and life safety standards without extensive investment in infrastructure that would require appropriated dollars".
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"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 U.S. government", the statement added.
The new embassy is certainly in a less-central and less-prestigious location in London.
The new building will open for business on January 16.
Bemused construction workers and passers-by took selfies with the Trump waxwork, which was first unveiled at Madame Tussauds in January previous year.
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Leading Brexit campaigner Nigel Farage, who visited Trump following his election, said it was "disappointing" the president could not visit when he had been to so many other countries.