Downing Street said its position had not changed on the US president's trip as Theresa May came under pressure to downgrade or axe the visit.
“An invitation has been extended and accepted,” a Number 10 spokesman said, stressing the position had not changed.
Ministers face being hauled into the Commons later amid continued concerns about the impact on Britons, as well as the way the Government has responded.
The Foreign Office said Britons with dual citizenship would be exempt from the controversial travel ban, but UK residents have been caught up in the chaos.
The US president accepted an invitation to visit Britain later this year, where he is due to be hosted by the Queen and would be treated to all the pomp and ceremony accorded to a state visit.
But more than one million people have signed a petition stating Mr Trump should not be given a state visit and it will now be considered for debate by MPs.
Labour, the Liberal Democrats and the SNP have called for the lavish state visit to be cancelled and Tory MPs have warned against allowing it to go ahead.
Conservative former foreign office minister Alistair Burt said the “optics of a visit are currently very bad” and suggested American officials should find a way for it not to go ahead.
Labour MP Dan Jarvis said it was “very likely” there would be an urgent question in the House of Commons on Monday to discuss the travel ban.
Demonstrators are planning to protest against the policy outside Downing Street and across the country on Monday evening.
The US president's team told Foreign Secretary Boris Johnson that Britons who have shared nationality with one of the seven mainly-Muslim countries covered by the restrictions would not be stopped from entering America.
But UK dual citizens travelling to the United States directly from one of the banned countries will face extra checks.
Mr Johnson spent Sunday speaking to the president's senior adviser Jared Kushner and chief strategist Stephen Bannon about the implications of immigration curbs.
His officials later issued guidance about what the border clampdown means for the UK.
The statement said:
- The ban applies to only individuals travelling from one of the seven named countries - Iraq, Iran, Libya, Somalia, Sudan, Syria and Yemen.
- Travellers to the US from anywhere other than one of those countries will experience no extra checks, regardless of nationality or place of birth.
- UK nationals travelling from one of those countries are not included in the ban, even if they were born in one of the affected states.
- Dual citizens from one of the seven countries travelling to the US from outside those countries are not affected.
- Dual nationals might have extra checks if they travel directly from one of the seven countries.
Mr Johnson had earlier branded Mr Trump's controversial policy, which includes a bar on all refugees, “divisive and wrong”, and criticised the decision to “stigmatise” people based on their nationality.
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