"In the tweet, Trump blames his predecessor, former president Barack Obama, for the decision to sell the existing embassy, which he describes as "the best located and finest" in the city, for "'peanuts'".
Trump accepted a separate invitation for an official state visit when he met Prime Minister Theresa May a year ago.
The move to relocate the US embassy to Nine Elms has been in the works for years, stretching back to 2008 when the State Department under President George W. Bush announced that it signed an agreement with a real estate developer to purchase the property.
The US President was due to make his first trip to Britain since being elected previous year, however he took to social media to say the date was off.
Mr Trump had been due to cut the ribbon on the new facility near Battersea Power Station in South London - but will instead send Secretary of State Rex Tillerson to perform the duty.
At the time, the PM said Trump was "wrong" to retweet the videos, and the USA president hit back at May on Twitter by telling her to focus on "destructive radical Islamic terrorism" in the United Kingdom, rather than on him.
"Many Brits who love America and Americans will see this as a betrayal of the special relationship between our two countries", Khan said in a statement.
The official drew a distinction between the State visit, which would include a visit with Queen Elizabeth II and royal trappings like a horse parade, and a working visit, that would include a meeting with Prime Minister Theresa May and other diplomatic formalities like opening the embassy.
In November, Ms May directly criticised Mr Trump's decision to retweet material from the far-right extremist group, Britain First.
The latest development followed reports that Mr Trump wanted to delay a potential visit amid concerns about large-scale protests.