The statement reported by the Press Association came shortly after May’s return from Turkey, following her trip to the White House as the first foreign head of state Trump welcomed.
During both visits, she refused to condemn his executive order to ban refugees from entering the U.S.
May’s silence was largely criticized by the British public, media and lawmakers, including MPs from her Conservative party.
Labour Party leader Jeremy Corbyn said on Twitter: "@theresa_may hand in hand with the man who banned @Mo_Farah & Tory MP @nadhimzahawi. Yet she remains silent."
Baroness Hussein Ece wrote that May’s reaction was late.
“This should've been said hours ago & not finally responding to pressure from the public,” Ece said.
Nadhim Zahawi, an MP from leading Conservative Party said on social media that he was informed that he would be affected by the ban because of his Iraqi origin.
“I'm a British citizen & so proud to have been welcomed to this country.
“Sad to hear ill be banned from the USA based on my country of birth,” Zahawi wrote.
May was asked repeatedly whether she would condemn the ban during a press conference in the Turkish capital, Ankara with Prime Minister Binali Yildirim on Saturday.
"The United Kingdom is responsible for the United Kingdom's policy on refugees,” May said in Ankara.
"[This] 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."