She says the idea that Trump is going after Khan because he's a Muslim is "utterly ridiculous".
"So you think the mayor of London is at fault for what happened?"
"It's even more important that we work together with our allies and our friends and our partners - yes, to keep us safe, but also to expand our understanding of what we can achieve together", Clinton said.
A day after bombings in NY and New Jersey, Khan tells The London Standard that attacks are "part and parcel" of life in major cities.
Khan has pushed back, calling Trump bigoted and saying that he doesn't need advice from the US President.
Eight minutes later, he tweeted, "Whatever the United States can do to help out in London and the U".
"Notice we're not having a gun debate right now, because they didn't kill with guns".
But the mayor actually said the public didn't need to be anxious about the increased police presence in the city. "There's no reason to be alarmed". "One of the things the police, all of us need to do is make sure we're as safe as we possibly can be", Khan said.
Sen. Susan Collins of ME, a Republican member of the Senate intelligence panel, said the ban was "too broad" but agreed with Trump that better immigration procedures are needed.
Khan says that London residents should expect to see an intensified police presence in the wake of the attacks.
The war of words between the two leaders intensified further Monday evening after Trump criticized Mayor Sadiq Khan's response to the London Bridge terrorist attack in two tweets, and the mayor said Trump should not be welcomed in the capital. "I condemn it in the strongest possible terms".
May's cowardice and lack of political will to call out Trump's hate is yet another example of how bigotry has been mainstreamed in our political and public discourse.
The Islamic State group later claimed responsibility.
"At least 7 dead and 48 wounded in terror attack and Mayor of London says there is "no reason to be alarmed!" Trump tweeted, several hours after promoting his controversial travel ban as an extra level of security for Americans in light of the attack.
Trump added that the media "is working hard to sell it!"
Trump said he had spoken with May to express America's "unwavering support" and offer USA assistance as the British government works to protect its citizens and bring the guilty to justice.
He denied he was stoking up a feud which went back to 2016, when the mayor described the then presidential candidate's calls for a ban on Muslim entry into the U.S. as "ignorant".
May on Monday refused to explicitly criticize the president.
Mr Khan has come under repeated criticism from Donald Trump over his handling of the terror attacks.
Trump's tweets have been heavily criticized by a number of British politicians, who are now preparing for the country's general election which is scheduled to take place on Thursday.
US President Donald Trump, speaks as he attends a meeting with EU leaders at the European Council, in Brussels, Belgium on Thursday May 25, 2017. "I think one of the things, when you have a special relationship, it's no different to when you've got a close mate. Why would you want to stop them coming?" "President Trump's attack on him is unacceptable".
"Trump is an embarrassment to America", he said.