Donald Trump's border clampdown is "divisive" and the Government is concerned about its impact on Britons, a Treasury minister has said.
The UK will make representations to the US if the travel ban on refugees and citizens from seven mainly-Muslim countries hits British travellers, David Gauke said.
Downing Street was forced to issue a midnight statement as it attempted to calm the growing backlash after Theresa May repeatedly refused to criticise President Trump's controversial move.
It said the Prime Minister did "not agree" with the ban and would act to help UK citizens.
Mr Gauke told BBC One's The Andrew Marr Show: "There is a particular concern that has emerged over the course of yesterday over the implications for British nationals, which is particular concern for us."
He added: "We disagree with the position President Trump has set out."
Mr Gauke said the row showed how important Britain's relationship with the US is because the Government needed "to have influence" on Washington.
He added: "The Prime Minister is not a shoot from the hip type of politician. She wants to see the evidence. She wants to understand precisely what the implications are."
Conservative MP Nadhim Zahawi, who was born Baghdad in Iraq, said he felt demeaned and discriminated against after being told he would be hit by the ban.
"For the first time in my life last night I felt discriminated against, it's demeaning, it's sad," he told the programme.