The prime minister was criticised for refusing to condemn President Trump's executive order on Saturday.
It halted all refugee admissions and has temporarily barred people from seven Muslim-majority countries.
At an earlier news conference in Turkey, Mrs May said it was up to the US to decide its own policy.
Mr Trump has also banned Syrian refugees indefinitely and suspended visas for people from six other countries.
The PM's refusal to openly challenge the ban had prompted criticism from politicians, including Conservative MPs.
Heidi Allen, Conservative MP for South Cambridgeshire, said on Twitter: "Strong leadership means not being afraid to tell someone powerful when they're wrong."
Labour's Jeremy Corbyn said Mrs May showed "weak failure" in standing up for British values.
"President Trump's executive order against refugees and Muslims should shock and appal us all," he added.
A holidaymaker from Glasgow says she is "upset" and "afraid" after being refused boarding for her flight home to Scotland.
Hamaseh Tayari, who holds an Iranian passport, was due to fly from Costa Rica to New York, and then from New York to Glasgow, but was stopped due to the ban.
She said staff at San Jose airport in Coast Rica were sympathetic but that "it's a crazy thing that I really didn't expect to happen to me."
Another Conservative MP, Nadhim Zahawi, who is of Iraqi origin, said a US immigration lawyer had told him he would be affected by the ban.
"A sad sad day to feel like a second-class citizen," he said. "Sad day for the USA."
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."
At a news conference in Ankara with Turkish Prime Minister Benali Yildirim on Saturday, Mrs May said the US was responsible for its own refugee policy.
She added: "The United Kingdom is responsible for the United Kingdom's policy on refugees.
"[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."
Theresa May does "not agree" with Donald Trump's refugee ban and will appeal to the US if it affects British citizens, Downing Street has said.