Iranian Foreign Ministry spokesman Bahram Qassemi called on certain states to stop "pursuing their short-term political and economic goals, which seem to be strategic, in favor of security for their citizens as well as the entire world".
A spokesman said: "We ask you to be vigilant and report anything that you see or hear which is suspicious, or just doesn't feel right".
Many people on social media reacted angrily to Trump's comments, accusing him of being unpresidential and taking the London Mayor's comments out of context.
Khan in his statement condemned the "cowardly" attacks.
"There is no justification whatsoever for such barbaric acts", Khan said, adding that "there's no reason to be alarmed" over an increased police presence.
British Prime Minister Theresa May on Sunday announced that the June 8 General Election will go ahead as planned despite another terrorist attack in London as she blamed the "evil ideology of Islamist extremism" for the three terror attacks in the country.
This is not the first time Trump has criticised Khan, who became the first Muslim mayor of a major European city when he was elected into office in May previous year.
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It comes after seven people were killed and 48 others were injured when the three attackers targeted those out on Saturday night.
It is at this point that armed officers confronted the three male suspects, who were shot and killed in Borough Market.
London's Metropolitan Police said armed officers were at two scenes - on the bridge and the nearby Borough Market, a busy area of restaurants and bars.
The Metropolitan Police confirmed that they had arrested 12 people in connection to the attack.
"We cannot and must not pretend that things can continue as they are", she said, adding that "difficult" and potentially "embarrassing" conversations were needed within the United Kingdom about dealing with the spread of extremism.
She said the investigation was fast moving and expressed gratitude to the police and emergency services who were at the scene. Britain was already on edge after a suicide bombing two weeks ago at an Ariana Grande concert in Manchester, in northwest England, that killed 22 people and injured dozens more.
May said the country is "experiencing a new trend in the threat we face as terrorism breeds terrorism".