The US presidential hopeful had said in an interview to the 'The New York Times' that he was happy to see Khan take over his new post and that "there will always be exceptions" to his controversial Muslim ban comments.
"This isn't just about me. It's about my friends, my family and everyone who comes from a background similar to mine, anywhere in the world," Khan said in his rebuttal.
"Trump's ignorant view of Islam could make both our countries less safe -- it risks alienating mainstream Muslims around the world and plays into the hands of the extremists. Donald Trump and those around him think that western liberal values are incompatible with mainstream Islam -- London has proved him wrong," the 44-year-old newly-elected mayor added.
Khan told the BBC he is supporting Democratic candidate Hillary Clinton in her bid for the White House: "I hope she trounces him (Trump)."
Last year, 69-year-old Trump had called for a temporary halt to all Muslims entering the US in the wake of the deadly terror attack in San Bernardino, California.
He said many Muslims nursed a "hatred" towards America and a ban should be in force "until our country's representatives can figure out what is going on".
Labour MP Khan, the son of a Pakistani bus driver, had likened to Trump's campaign with the Conservative party's tactics in the mayoral elections.
"They (Conservatives) used fear and innuendo to try to turn different ethnic and religious groups against each other -- something straight out of the Donald Trump playbook," he wrote in an article after being sworn in to his post over the weekend.
Khan officially took charge of City Hall in London on Saturday following Thursday's election, which saw him defeat his Conservative rival Zac Goldsmith by 1,310,143 votes to 994,614 -- giving him one of the largest personal mandate for any UK politician.
Is the Modi government scared of this man?
'We must question how we are bringing up our sons'
Is the Modi government scared of this man?