Politicians condemned Trump for attacking Khan after the incident, that saw three jihadis go on a stabbing rampage on Saturday night, killing seven and injuring 48.
His tweet took Khan’s comment that Londoners had “no reason to be alarmed” about the increased police presence out of context.
As Khan said he had “better things to do” than respond, he was backed by American politicians, including New York mayor Bill De Blasio.
But May refused to condemn Trump despite the growing outrage.
Pressed by reporters, May said on Monday that Khan “is doing a good job and it’s wrong to say anything else.”
Even when asked whether she would welcome “a period of silence” from Trump, May said: “I’m very clear that Sadiq Khan is doing a doing job as mayor of London.”
But now May has spoken out to say, in guarded terms, that Trump was “wrong”.
She also said the planned state visit by Trump will go ahead, despite Khan’s opposition.
She told The Sun: “The relationship with America is our deepest and most important defence and security relationship.
“Having said that, I think Donald Trump is wrong in what he said about Sadiq Khan, in relation to the attack on London Bridge.”
She added: “We’ve been working with Sadiq Khan. When you’re working in the aftermath of an attack like that, party politics is put to one side.”
After Trump’s tweet, a spokesperson for Khan said:
“The Mayor is busy working with the police, emergency services and the government to coordinate the response to this horrific and cowardly terrorist attack and provide leadership and reassurance to Londoners and visitors to our city.
“He has more important things to do than respond to Donald Trump’s ill-informed tweet that deliberately takes out of context his remarks urging Londoners not to be alarmed when they saw more police - including armed officers - on the streets.”
Khan was backed by predecessor Boris Johnson, who said he was “perfectly right to reassure the public about the presence of armed officers on the street”.
But Johnson also said he there was “no reason” to cancel Trump’s state visit.
Khan told Channel 4 News on Monday that the country should not “roll out the red carpet to the President of the United States in the circumstances where his policies go against everything we stand for”.
At Monday’s White House press briefing, Deputy Press Secretary, Sarah Sanders, repeatedly denied that Trump was “picking a fight” and was merely trying to draw attention to the threat posed by terrorists.