LONDON: British Prime Minister Theresa May said on Saturday Britain did not agree with US President Donald Trump's curbs on immigration after facing criticism from lawmakers in her own party for not condemning his executive order.

On a visit to Turkey, she was asked three times to comment on Trump's move to put a four-month hold on allowing refugees into the United States and temporarily barring travellers from Syria and six other Muslim-majority countries, which he said would protect Americans from violent Islamists.

She replied Washington was responsible for its policy on refugees.

But later, after her return to London, her spokesman said: "Immigration policy in the United States is a matter for the government of the United States, just the same as immigration policy for this country should be set by our government.

"But we do not agree with this kind of approach and it is not one we will be taking. We are studying this new executive order to see what it means and what the legal effects are, and in particular what the consequences are for UK nationals."

Trump's executive order plunged America's immigration system into chaos, with legal US residents being turned away at airports, and drew criticism from US Western allies including France and Germany.

May, who became the first foreign leader to meet the president following his inauguration last week, had been enjoying a positive response at home for revitalising the "special relationship" between the United States and Britain.

But her response while in Ankara for talks with Turkish President Tayyip Erdogan triggered criticism from her party.

"Trump really is a sickening piece of work," lawmaker Sarah Wollaston, a member of May's Conservative Party, said on Twitter. She said Trump should be snubbed by parliament when he comes for a planned state visit to Britain later this year.

"I don't care how special the relationship is, some lines just shouldn't be crossed," Conservative lawmaker Heidi Allen said in a tweet. "Strong leadership means not being afraid to tell someone powerful when they're wrong. It's an ethos this country is proud of."

A third Conservative member of parliament, Nadhim Zahawi, said he would be banned from the United States as a British citizen of Iraqi origin.

"A sad sad day to feel like a second class citizen," he tweeted. "Sad day for the USA."

Jeremy Corbyn, leader of the main opposition Labour Party, said May should have stood up to Trump.

"It should sadden our country that she chose not to," he said.