Mr Khan had in fact said people should not be alarmed by an increased police presence. During the USA presidential election campaign, Khan was among many people who spoke out against Trump's proposed ban on Muslims entering the United States, an idea he said would play into the hands of extremists.
The president's tweets come as London grapples with the aftermath of the attack and Khan tries to explain that the religious beliefs of the terrorists involved are not the same beliefs embraced by him and most of the world's 1.6 billion Muslims.
Khan told Channel 4 that there were "many things" that the US President was wrong about, and that the state visit should not go ahead.
On Monday, one of the world's biggest news organizations made a remarkable statement: President Trump can not be trusted to give accurate information about a terrorist attack.
During a visit to Chicago in September a year ago, Khan endorsed Trump's opponent, Hillary Clinton.
Police say 27-year-old Khuram Shazad Butt and 30-year-old Rachid Redouane are two of the three attackers who executed the deadly rampage.
The controversial policy has been blocked by lower courts, citing various reasons, including the statements Trump made during the 2016 campaign.
"Sadiq Khan was saying something very reasonable and sensible about how there was no reason for the public to be alarmed by the presence of armed officers on the streets", he said.
The three men killed seven and injured 48 people on Saturday evening; 36 people remain in hospital, 18 in critical condition.
"One of the things about having close mates and having a special relationship is to not just stand with them in adversity but call them out when they are wrong".
"Try to imagine the United Kingdom prime minister attacking the Mayor of NYC the day after 9/11", said European Parliament cabinet member Simon O'Connor.
Clinton slammed the sitting president's politics by saying, "We are not living in normal times", before praising the London mayor's leadership.
After Trump's first attack on Khan, the acting United States ambassador to the UK, Lewis Lukens, notably singled out the London Mayor for praise.
Trump, however, doubled down on his attack Monday morning. "We will never let these cowards win and we will never be cowed by terrorism".
Trump's son, Donald Trump, Jr., resurfaces that September tweet after an attack at Westminster.