The Prime Minister initially dodged questions about her view on the controversial move but later, when pressed, insisted it was up to America to devise its own policy.
But during a joint press conference in Ankara, her Turkish counterpart Binali Yildirim hit out at the ban, warning the US that building a wall would not solve the crisis.
Mrs May said: “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.”
Liberal Democrat leader Tim Farron attacked the PM for refusing to condemn the ban.
He 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.
“Not only is this shocking even by her standards, it cannot be allowed to stand. The President’s actions have horrified the world, and this is a moment when she has to show what side she is on.
“Perhaps she feels in a weak position on Syrian refugees because her own record on this is so lamentable.
“More likely it is because she is so desperate for a trade deal at any price after her decision to haul Britain out of the world’s largest market that she will turn a blind eye to anything.
“At the press conference she contrived to make the Turkish government look liberal. They said it was wrong to build walls. Rather than fighting to build a world that is open, tolerant and united, Theresa May is dividing the world in a very dangerous way.
“If Theresa May would stay in the single market none of this humiliation would be necessary.”