A baby-shaped blimp meets a thin-skinned president: cue the renewal of a war of words between Donald Trump and London's first Muslim mayor , encompassing terrorism, crime and good manners.

Mayor Sadiq Khan has "done a very bad job on terrorism", Trump declared, linking immigration to a deadly wave of knife crime in London, as he began a contentious four-day trip to Britain this week.

"You have a mayor who has done a terrible job in London," he said in an interview with Friday's edition of The Sun newspaper.

It was the latest potshot in a feud that began when Khan, the son of a bus driver who emigrated from Pakistan in the 1960s, criticised Trump's travel ban on people from certain Muslim countries.

Khan responded Friday by saying terrorism was a global problem which also affected other European cities.

"What is interesting is Trump is not criticising mayors of those cities, but he is criticising me," he told BBC radio.

Trump's comments blaming immigration for crime in England were "preposterous", he said.

The president ridiculed Khan in June last year following the latest in a spate of terror attacks in London.

Distorting a message from Khan, telling Londoners there was "no reason to be alarmed" by an increased police presence, Trump tweeted: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!'"

At the time, Khan criticised Trump as "ill-informed" and on Friday, lauded the "special relationship" between Britain and the United States.

Asked if the new row could jeopardise that bond, he said: "It takes two to tango, and I'm not tweeting President Trump or saying beastly things about him."

Pigs and babies

Khan added: "I think our prime minister (Theresa May) should have the confidence to speak to the US president on equal terms and it's for President Trump to say what he wants about me; I'm not going to rise to President Trump's views."

Khan is a member of the opposition Labour party. His predecessor as London mayor was the Conservative Boris Johnson, who resigned this week as foreign secretary in protest at May's blueprint for Brexit.

In his Sun interview, Trump accused May of violating British voters' wishes with the plan and, for good measure, praised Johnson as an alternative prime minister.

If Johnson and Trump are kindred spirits politically, Khan this week authorised a plan by protestors to float a six-metre (19-foot) inflatable of a distinctly orange nappy-clad baby bearing Trump's face above London's Parliament Square on Friday.

Trump's attack on May's Brexit plan drew scorn from across the political divide as being ill-mannered during a high-profile visit. But the president told The Sun that Khan himself had "not been hospitable to a government that is very important".

"Now he might not like the current president, but I represent the United States," he said, insisting that "millions" of Britons supported his hard line on immigration.

The London mayor has powers over policing and transport in the capital of eight million people, but does not control immigration policy, which is set nationally by the Home Office.

Khan's authorisation for the "angry baby" stunt has infuriated Trump supporters in Britain such as Brexit champion Nigel Farage, who called it an "insult".

Conservative MP Michael Fabricant was accused of Islamophobia after tweeting a cartoon showing the Muslim mayor 's head on an inflatable balloon, engaged in a sex act with a pig. Fabricant later deleted the tweet and apologised.

But the war of words escalated as Labour lawmaker David Lammy said Trump's real problem with Khan was not about policy but the mayor's faith.

"He hates that London chose a Muslim mayor . The President is racist. He does not deserve to meet our Queen today #StopTrump," he tweeted.