Plans for a state visit by President Donald Trump to the UK have not been cancelled in the wake of his retweeting of far-right videos, a senior Cabinet minister has indicated.

The Government is facing growing demands for the invitation to be withdrawn after tweets from the president which included a direct rebuke to Prime Minister Theresa May.

London Mayor Sadiq Khan said Mrs May should cancel the visit and demand an apology on behalf of the British people from the president, while Liberal Democrat leader Sir Vince Cable branded Mr Trump an "evil racist" who should not be given the honour of a state visit.

But responding in the House of Commons to a string of demands for the visit would be called off, Home Secretary Amber Rudd said only: "The invitation for the visit has been extended and accepted but the dates and precise arrangements have yet to be agreed."

Ms Rudd repeated Downing Street's statement that Mr Trump was "wrong" to spread the messages of far-right group Britain First on Twitter.

But the Home Secretary urged critics of the president to remember the importance of the trans-Atlantic alliance to Britain when voicing their concerns.

Ms Rudd denounced Britain First as "an extremist organisation which seeks to divide communities through their use of hateful narratives which spread lies and stoke tensions".

She added: "President Donald Trump was wrong to retweet videos posted by the far-right group Britain First."

Mr Trump caused outrage on Wednesday by retweeting three posts by Britain First deputy leader Jayda Fransen to his 43.6 million followers, including footage from the Netherlands purporting to show a Muslim migrant attacking a man on crutches.

Communities Secretary Sajid Javid said Mr Trump had "endorsed the views of a vile, hate-filled racist organisation that hates me and people like me", adding: "He is wrong and I refuse to let it go and say nothing."

The Prime Minister's official spokesman said on Wednesday that Britain First was dedicated to causing division among communities and that the president had been "wrong" to share the posts.

Number 10's comments appear to have sparked a virtually unprecedented social media rebuke by a head of state to the leader of a close ally, as Mr Trump used an early-morning tweet addressing Mrs May directly.

The president wrote: "@Theresa_May, don't focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom. We are doing just fine!"

Responding to the latest tweets, Education Secretary Justine Greening said Mr Trump is "a president that behaves unlike any other" and added she did not agree with his comments.

Shadow foreign secretary Emily Thornberry said Mr Trump's tweets were designed to "humiliate and belittle" the Prime Minister and had put the Queen in a "very difficult and invidious position" as the host for the planned state visit.

"If he comes next year, a year which is supposed to be a really happy year for the royal family, what on earth are people supposed to make of it?" asked Ms Thornberry.

She told BBC Radio 4's Today programme that Mrs May was "absolutely right" to criticise Mr Trump's initial tweet, but added: "There are Americans who are our friends, we share many values with America. But we don't share values with this man."

Ms Rudd urged MPs to bear in mind the danger of damaging relations between the US and UK in their comments, telling the Commons: "When we look at the wider picture of the relationship between the UK and America, I know how valuable the friendship is between our two nations.

"And as Home Secretary, I can tell the House that the importance of the relationship between our countries and the unparalleled sharing of intelligence between our countries is vital. It has undoubtedly saved British lives.

"That is the big picture here, and I would urge people to remember that."