British Prime Minister Theresa May insists she is not afraid to criticise a key ally, saying US President Donald Trump's retweets of a "hateful" far-right group were "the wrong thing to do".

But May's government dug in its heels over mounting calls to cancel Trump's planned state visit to the UK -- a revoke of an invitation that would put Queen Elizabeth II in a difficult position.

Trump's retweeting of anti-Muslim videos from far-right fringe group Britain First has been widely condemned in Britain.

May's spokesman called the retweets "wrong," and the prime minister gave the same verdict overnight.

"The fact that we work together does not mean that we are afraid to say when we think that the United States have got it wrong and to be very clear with them," May said.

"I am very clear that retweeting from Britain First was the wrong thing to do."

The responding tweet by the Dutch embassy in Washington. (Photo: AP).

Speaking in Amman, Jordan, May said the anti-Islam, anti-immigrant group was "a hateful organisation" that runs counter to "common British decency."

Trump responded to criticism from Britain with a tweet urging May to focus on "the destructive Radical Islamic Terrorism that is taking place within the United Kingdom," rather than on him.

May countered that "we take the need to deal with the terrorist threat very seriously."

May has sought to cultivate a close relationship with Trump, visiting him in Washington days after his inauguration in January and extending the offer of a state visit hosted by the Queen.

But the Twitter storm has prompted renewed calls for the trip to be called off, which the Associated Press reports would require teh queen to rescind the invitation.

In Britain's constitutional monarchy, the queen invites foreign leaders to state visits — regarded as a great honour — on the advice of Britain's Foreign and Commonwealth Office.

In Trump's case, it was May who extended the invitation on the queen's behalf just days after Trump assumed office. While no date has yet been set for the visit, both governments say the state visit is still on.

Trump had already faced strong opposition in Britain over his attempt to ban travel to the US from several majority-Muslim countries.

In the House of Commons overnight, multiple lawmakers stood to demand that the visit be scrapped.

London Mayor Sadiq Khan also joined the calls. He said Trump had promoted "a vile, extremist group" and an official visit by him to Britain "would not be welcomed."

May said the visit was still on — though she suggested it was not imminent.

"An invitation for a state visit has been extended and has been accepted," she said. "We have yet to set a date."

The retweets by Trump, who has almost 44 million Twitter followers, provided a huge boost to Britain First. The tiny but publicity-savvy group has staged direct-action protests at mosques and is active on social media. The group regularly posts inflammatory videos purporting to show violence by Muslims, without context or supporting information.

Several lawmakers called Thursday for the group to be banned.

Home Secretary Amber Rudd said that "British people overwhelmingly reject the prejudiced rhetoric of the far right."

"This government will not tolerate any groups that spread hate by demonizing those of other faiths or ethnicities," she said.

Rudd also welcomed a suggestion by Conservative lawmaker Peter Bone that Trump delete his Twitter account.