Prime Minister Theresa May has been criticised for refusing to condemn President Donald Trump's ban on refugees entering the US.
Asked repeatedly about the issue during a news conference in Turkey, Mrs May said only that it was up to the US to decide its own policy.
Mr Trump has banned Syrian refugees indefinitely and suspended visas for people from six other countries.
Labour's Jeremy Corbyn said she should have stood up for British values.
Mrs May told reporters: "The United States is responsible for the United States' policy on refugees.
"The United Kingdom is responsible for the United Kingdom's policy on refugees and our policy on refugees is to have a number of voluntary schemes to bring Syrian refugees into the country, particularly those who are most vulnerable, but also to provide significant financial contributions to support refugees in countries surrounding Syria."
Mrs May was speaking at a news conference in Ankara with Turkish Prime Minister Benali Yildirim.
MPs have rounded on her for not openly condemning Mr Trump's policy.
Mr Corbyn said: "President Trump's executive order against refugees and Muslims should shock and appal us all.
He added: "After Trump's hideous actions and May's weak failure to condemn them, it's more important than ever for us to say to refugees seeking a place of safety, that they will always be welcome in Britain."
Conservative peer Baroness Warsi wrote on Twitter: "The moment we once again lost a little more moral authority. The hypocrisy of the debate on #Britishvalues becomes more stark by the day."
By Laura Kuenssberg, BBC News political editor
Before this trip Theresa May promised to be frank with the American president when she disagreed. But when pressed for an answer on Donald Trump's controversial refugee ban she first of all, uncomfortably, avoided the question.
Then on the third time of asking she would only say that on the United States policy on refugees it was for the US. Her refusal to comment was immediately condemned by the former Labour leader, Ed Miliband, who said it was shocking and wrong. The UN has expressed dismay and France and Germany have reported concerns.
Downing Street had been delighted with its visit to Washington. But the PM returns to a row over her refusal to give her view.
Having boasted that the virtue of the special relationship is that friends can be candid with each other, Theresa May's silence on President Trump's executive order will raise suspicion that in fact, as the junior partner, she is unwilling to speak her mind.
Liberal Democrat leader Tim Farron said: "Theresa May has failed to criticise President Trump for turning away and banning refugees whose only crime is to believe in a different religion."
Conservative MP Sarah Wollaston said Mr Trump should not be invited to address both MPs and peers on his state visit to the UK.
She said such an honour should be reserved for leaders who have made an outstanding, positive difference in the world, adding: "That doesn't include Mr Trump."
Scottish Labour leader Kezia Dugdale said it was "simply shameful that the prime minister had not condemned his actions, adding: "It is heart-breaking to hear that some of the most vulnerable people in the world are being turned back."
Responding to the criticism, Downing Street said: "Mrs May has said repeatedly that there will be issues on where we disagree on domestic policies. That is nothing new; the special relationship allows us to have frank conversations at all times."
Mrs May was in Turkey for talks with President Erdogan and Prime Minister Mr Yildirim having met the US president on Friday.
Asked about Mr Trump's changes to immigration policy, Mr Yildirim said the only way to tackle the refugee crisis was to deal with the reasons people were fleeing.
He said: "You cannot solve this issue of refugees by putting up walls. You have to eradicate the root causes of this. You have to eradicate the regional discrepancies in terms of development."