In the television interview on Sunday morning, Khan said the United Kingdom general election, scheduled for Thursday, should go ahead as planned.
Law enforcement officials in major USA cities said they were not aware of any threats but were on alert.
"We have long collaborated with policymakers civil society, and others in the tech industry, and we are committed to continuing this important work".
She added that the measures were needed as "terrorism breeds terrorism" and attackers copy each other.
They said: "We would at this point also like to reach out to those affected by the London terror attack, sending our love and condolences to those who have lost loved ones, our hearts are aching for your loss, may those injured have a speedy recovery".
The secretary general of the Muslim Council of Britain, Harun Khan, also condemned the attack.
The attack Saturday came on the eve of a benefit concert by Grande for victims of last month's Manchester Arena bombing in aid of the victims and their families. "Today, we will all grieve for their loss". Searches there continued, police said, suggesting that they had identified at least one assailant.
Britain's official terrorism threat level was raised from "severe" to "critical" after the Manchester attack, meaning an attack may be imminent.
She refused to say whether the attackers had been known to the authorities before Saturday.
The Conservatives were far ahead in polls but their lead has narrowed in recent days. "We have no specific information that Scotland is at risk of attack and I would ask you to go about your business as normal, remaining alert but not alarmed".More news: Vote Labour to stop independence referendum - Gordon Brown
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"The mayor is busy working with the police, emergency services and the Government to co-ordinate the response to this horrific and cowardly terrorist attack and provide leadership and reassurance to Londoners and visitors to our city".
"We believe three people were involved, but we still have got some more inquiries to do to be 100 percent confident in that", he said.
He also confirmed that an off-duty officer was also injured in the incident. Four are in a critical condition. "That this should happen in this month of Ramadan, when many Muslims were praying and fasting only goes to show that these people respect neither life nor faith".
The assault unfolded - and ended - quickly, with police fatally shooting the three attackers within eight minutes.
It was a remarkably rapid response that was bound to have saved many lives.
"It is unbelievable and unforgivable that the President of the United States of America should launch such a self-serving and cheap political attack on London's Mayor", said Wes Streeting, a Labour lawmaker.
The New York Police Department (NYPD) Counter-terrorism bureau said it was "deploying officers to heavily-travelled pedestrian locations across the city". Police shot and killed the attackers there.
The three attackers were wearing fake bomb vests, according to local media.
The National Health Service in England said 48 people were taken to various London hospitals after the attack.
He said he came upon the attackers and "hit one of them in the head with a basket and I knocked him out", Morariu told British TV. Many of those killed were children, and 116 people were injured. The evening's carnage carried grim echoes of a similar incident in late March, when a driver swerved into pedestrians at Westminster Bridge, another Thames crossing, killing four.