Republican presidential candidate Donald Trump, who has called for a temporary ban on Muslims entering the United States, suggested on Monday he would make an exception for London's newly elected Muslim mayor, the New York Times reported.

"There will always be exceptions," the Times quoted the real estate billionaire and presumptive Republican nominee as saying when asked how his controversial proposal would apply to Sadiq Khan, the son of a Pakistani immigrant bus driver and a seamstress, who was sworn in as London's mayor on Saturday.

Trump said he was happy to see Khan elected, the Times reported, adding: "You lead by example, always lead by example. If he does a good job...that would be a terrific thing."

Trump put forth the idea of the ban after deadly attacks by Islamist militants in Paris and California last year. Muslim and human rights groups, Trump's Democratic rivals and many of his Republican presidential opponents condemned the proposal as divisive, counterproductive and contrary to American values.

Khan, the Labour Party candidate, defeated his Conservative rival by a record margin to secure the biggest individual mandate in British political history after an acrimonious campaign.

Speaking of the Conservatives' tactics, Khan, 45, told Britain's Observer newspaper: "They used fear and innuendo to try to turn different ethnic and religious groups against each other – something straight out of the Donald Trump playbook."

In an interview with Time magazine, Khan said he wanted to go to the United States to see the interesting programmes the mayors of New York and Chicago were implementing, but that he would have to visit before January in case Trump won the November 8 election.

"If Donald Trump becomes the president I'll be stopped from going there by virtue of my faith, which means I can't engage with American mayors and swap ideas," Khan said.