Donald Trump should come to London to meet moderate Muslims who would challenge his "ignorant" views on Islam, Sadiq Khan has said.
The London mayor, who is a Muslim, has been involved in a public row with the presumptive Republican presidential nominee, who has called the Labour politician "rude" and "nasty".
Khan's clash with the White House hopeful followed Trump's call for Muslims to be banned from the US - although the presidential candidate has said he would allow the London mayor to visit the States.
Khan said: "Donald Trump last year said words to the effect that all Muslims should be banned from the USA and then when I was elected ... the day after he welcomed my election and said I would be the exception to his rule about Muslims going to the USA.
"My simple point was, 'I'm not exceptional'. What about my friends and family? What about Londoners who are businessmen and women who want to do business in America? What about Londoners who want to go and study in America but happen to be Muslim?
"What about Londoners who want to go on holiday in America or visit their family and friends who happen to be Muslim?
"I genuinely think that Donald Trump and his advisers' views on Islam are ignorant because the vast, vast, vast majority of Muslims are law-abiding and peaceful (and) unequivocally condemn these acts of terror committed by a small number of people using the name of Islam to justify their nihilistic actions."
He told LBC Radio: "My point to Donald Trump is this: because I am so confident that it is possible to be a mainstream Muslim, and for that to be compatible with Western, liberal values - we show this in London - come to London and see for yourselves that you can have Londoners who are Muslim, British, Western, are perfectly happy being both Western and Muslim.
"My invitation to him was come and meet me, my family, my friends, Londoners, who will show hopefully that his views on Islam are ignorant."
Trump told ITV's Good Morning Britain on Monday there would "always be exemptions" to the ban but he said he would "remember" the hostile reaction from the London mayor.
"He doesn't know me, hasn't met me, doesn't know what I'm all about. I think they were very rude statements and, frankly, tell him I will remember those statements. They are very nasty statements," he told the programme.
"When he won I wished him well. Now, I don't care about him, I mean, it doesn't make any difference to me, let's see how he does, let's see if he's a good mayor."
The presidential hopeful said the policies he mooted on the campaign trail were just "suggestions", but added that there was a "tremendous" problem with Islamic extremism.