Calls are being made to cancel a proposed state visit to the UK by President Trump after he clamped down on immigration to the US.
Labour leader Jeremy Corbyn said it would be "totally wrong" for the visit to go ahead later this year.
A petition to stop it has gathered nearly 900,000 signatures in a day, far more than the 100,000 needed for Parliament to consider a debate.
The visit was announced during PM May's trip to the US - no date has been set.
Downing Street was asked for a response to the calls to cancel. A spokesman said: "We extended the invite and it was accepted."
Buckingham Palace has declined to comment.
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Speaking on ITV's Peston on Sunday, Mr Corbyn said: "I think we should make it very clear we are extremely upset about it, and I think it would be totally wrong for him to be coming here while that situation is going on.
"I think he has to be challenged on this. I am not happy with him coming here until that ban is lifted, quite honestly."
Liberal Democrat leader Tim Farron backed the call. He said: "Any visit by President Trump to Britain should be on hold until his disgraceful ban comes to an end.
"Otherwise Theresa May would be placing the Queen in an impossible position of welcoming a man who is banning British citizens purely on grounds of their faith."
Alex Salmond, the SNP's foreign affairs spokesman, said he thought the state visit was "a very bad idea".
Also appearing on Sky News' Sophy Ridge, he said: "You shouldn't be rushing into a headlong relationship with the President of the United States."
Mr Salmond said reports Mr Trump was reluctant to meet Prince Charles during the visit were "an indication of the sort of enormous difficulties you get into when you hold somebody tight who is unpredictable, who has a range of views you find unacceptable."
And Mayor of London Sadiq Khan said the visit should not happen while the executive order was in place.
He told Sky News: "I am quite clear, this ban is cruel, this ban is shameful, while this ban is in place we should not be rolling out the red carpet for President Trump."
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Graham Guest, who started the petition, said he wanted it to "put the spotlight" on Mr Trump.
He told the Press Association: "A state visit legitimises his presidency and he will use the photo opportunities and being seen with the Queen to get re-elected.
"The wording in the petition is quite precise as I actually say that he should come here as the head of government to do government-to-government business.
"At the end of the day he is still the president and we've just got to live with that. But there's no reason why he should get all the pomp and publicity of a state visit."
'British values first'
Former shadow cabinet member Chuka Umunna also backed the calls to cancel the trip.
"State visits happen at the instigation of governments and, of course, you have got a prime minister who you want to have a decent working relationship with a US president.
"But they need to understand, just as they will put America first, we will put British values first."
Ruth Davidson, leader of the Scottish Conservatives, said she hoped Mr Trump would reconsider his position on immigration "immediately".
"State visits are designed for both the host, and the head of state who is being hosted, to celebrate and entrench the friendships and shared values between their respective countries," she said.
"A state visit from the current president of the United States could not possibly occur in the best traditions of the enterprise while a cruel and divisive policy which discriminates against citizens of the host nation is in place."
Paddy Ashdown, former leader of the Liberal Democrats, questioned the state visit on Twitter.
He wrote: "Am I alone in finding it impossible to bear that in pursuit of her deeply wrong-headed policies our PM is now forcing THAT MAN on our Queen?"
Conservative MP for Totnes, Sarah Wollaston, earlier tweeted that the US President should not be invited to address the Houses of Parliament, saying Westminster Hall "should be reserved for leaders who have made an outstanding positive difference in the world".