The embassy says the new building was funded entirely by the proceeds of the sale of other US government properties in London, not through appropriated funds.
Khan noted Trump's cancellation "reinforces what a mistake it was for Theresa May to rush and extend an invitation of a state visit in the first place".
"Bad deal. Wanted me to cut ribbon-NO!" the US president added.
But 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". 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.
But Trump said his decision, announced in a late-night tweet, was due to the president's concerns about the embassy's move from the tony Mayfair district to a far less fashionable area of London.
Trump tweeted overnight that he would not attend the ceremony, initially scheduled for next month.
His decision not to come was welcomed by critics outraged by the U.S. travel ban on Muslim-majority countries, and more recently, Trump's decision to re-tweet anti-Muslim videos posted by a British far-right organisation.
The mayor of London - who has been criticized by Trump in tweets - said Trump appeared to have "got the message from the many Londoners who love and admire America and Americans but find his policies and actions the polar opposite of our city's values of inclusion, diversity and tolerance".
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He said Trump's visit "would without doubt have been met by mass peaceful protests".
However, London's mayor Sadiq Khan, who has been a target of Mr Trump's twitter tirades, said the president had "got the message" that he was not welcome in the United Kingdom capital.
"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. "No date has been confirmed". Last month, Ambassador Woody Johnson, who was appointed by Trump, called it a "bargain".
"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", the statement added.
Asked about the PM's views on south London after the president described the embassy's new site as an "off location", the spokesman said: "I think Vauxhall is a vibrant and important part of London and home to many businesses".
There was an outburst on social media after the visit was announced a year ago, when protesters vowed to turn out in great numbers to let the US President know that he was not welcome in the UK.
Bemused construction workers and passers-by took selfies with the Trump waxwork, which was first unveiled at Madame Tussauds in January a year ago.