Trump also said that Khan had been foolishly nasty to him as "by far the most important ally" of the U.K. In a second tweet, Trump went on to compare Khan to New York's Mayor Bill de Blasio, who he called incompetent.
Trump continued the attack Monday, calling Khan a "stone cold loser".
Speaking directly to the US President as he arrived in Britain, Mr Khan claimed the US was "rolling back much of the progress made in previous decades".
In November 2017, Mr Khan also slammed Mr Trump for retweeting anti-Muslim propaganda from a British far-right party, and suggested Mrs May shouldn't welcome the U.S. president to the United Kingdom for a state visit.
Britain's relationship with the U.S. is an enduring alliance, but some British voters see Mr Trump as crude, volatile and opposed to their values on issues ranging from global warming to his treatment of women. A giant balloon depicting the US leader as a diapered baby floated over Central London and onto newspaper front pages around the world.
After lunch with the queen, Trump will be honored at extravagant state dinner at Buckingham Palace.
11 dead, 6 injured in shooting in Va. Beach; suspect dead
Craddock, 40, worked as a certified professional engineer for the city of Virginia Beach in its Public Utilities Department. The injured officer's life was saved when a bullet struck his vest, Chief Cervera told reporters.
In his video message Khan says: "President Trump, if you're watching this... your values and what you stand for are the complete opposite of London's values and the values in this country".
In a round of British newspaper interviews, he also recommended her successor walk away from talks with Brussels, refuse to pay Britain's agreed divorce bill and leave the European Union with no deal.
A sense of deja vu quickly spread around London as Trump barreled into the visit.
On Monday afternoon, the Queen presented her guests President Trump and the First Lady with some very lavish gifts during their official state visit.
Trump may also look to discuss a potential post-Brexit trade deal, telling reporters there was an "opportunity for a very big trade deal at some point" before he landed in the UK.
Meanwhile, at least 250,000 people are expected to protest in central London on Tuesday morning, on a route between Trafalgar Square and Parliament Square, when Trump meets May in Downing Street.
Trump is expected to face significant public protests in Britain as well as a royal welcome.
The 1959 crimson and gold-tooled book titled "The Second World War" by the late United Kingdom prime minister was given to Trump along with a three-piece pen set, CNN reported.