The Trump administration is standing firm over its ban on refugees from seven countries despite court rulings and mass protests against the move.
Mr Trump tweeted the US needed “extreme vetting, NOW”. His chief of staff said only 109 people, out of 325,000 travelling, had been detained.
The move has been widely condemned.
Sixteen state attorneys general have said the order is unconstitutional. One federal judge temporarily halted the deportation of visa holders.
Live: Protests over ban
Mr Trump’s executive order, signed on Friday, halted the entire US refugee programme for 120 days, indefinitely banned Syrian refugees, and suspended all nationals from seven Muslim-majority countries for 90 days.
Those who were already mid-flight were detained on arrival – even if they held valid US visas or other immigration permits. It is not known how many others were turned away at airports overseas as they tried to board flights to the US.
Thousands gathered at airports around the country to protest on Saturday, including lawyers who offered their services for free to those affected.
Further demonstrations are being held on Sunday – including one outside the White House.
Who is affected by the ban?
All travellers who have nationality or dual nationality of Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen are not permitted to enter the US for 90 days, or be issued an immigrant or non-immigrant visa.
This includes those who share dual nationality with allied countries, including the UK, although Canada has been told its dual nationals are not affected.
The UK foreign office put out a statement saying that only those dual nationals travelling from one of the blacklisted seven countries would be subject to extra checks – those travelling between the UK and US would not be affected.
However, one Scottish veterinary student – who travels on an Iranian passport – was unable to fly home from her holiday in Costa Rica because she was told her transit visa for the US was no longer valid.
White House Chief of Staff Reince Priebus said US green-card holders – legal residents – would also not be affected, although he admitted to NBC’s Meet the Press programme that they could be subject to greater questioning at airports.
Regarding those held at airports, he said: “Most of those people were moved out. We’ve got a couple of dozen more that remain and I would suspect that as long as they’re not awful people that they will move through before another half a day today.”
He said the seven countries had been chosen because they had already been identified by Congress and the Obama administration as the most likely to harbour terrorists, and he did not rule out the fact that more countries could be added to the list.
He rejected criticism that the implementation of the order had been chaotic.
Some leading Republicans expressed concern.
John McCain called it a “very confusing process” which would “probably, in some areas, give ISIS [Islamic State group] some more propaganda”, while Senate Majority Leader Mitch McConnell said it was important to remember that “some of our best sources in the war against radical Islamic terrorism are Muslims”.
Democrats Senate Majority leader Chuck Schumer said the US now appeared “less humanitarian, less safe, less American” and said the Democrats would introduce legislation to overturn it.
Fear, uncertainty and small acts of rebellion at Dulles airport
Ali worked for three years as an interpreter for the US Army and gained admittance to the US through a Special Immigrant Visa, reserved for Iraqi and Afghan nationals who face threats of violence for working for Americans during the conflicts there.
He now has a green card, and returned to Iraq for his father’s funeral, only to be delayed for hours for questioning at Dulles.
“We are not terrorists. We are not bad people,” said Ali. “It’s so hard. I hope they will change their minds on this position.”
Read more from the BBC’s Jessica Lussenhop on the night at Dulles airport, near Washington
Legal minds have their say
In a joint statement, 16 attorneys general, from states including California, New York and Pennsylvania, said they would “use all of the tools of our offices to fight this unconstitutional order” and, until it was struck down, would “work to ensure that as few people as possible suffer from the chaotic situation that it has created”.
Late on Saturday, federal Judge Ann Donnelly, in New York, ruled against the removal from the US of people with approved refugee applications, valid visas, and “other individuals… legally authorised to enter the United States”.
The emergency ruling also said there was a risk of “substantial and irreparable injury” to those affected.
She was ruling on a case brought by the American Civil Liberties Union (ACLU) on behalf of two Iraqi men with links to the US military who were detained at JFK Airport in New York.
Both have now been released. Another court hearing is set for February.
Elsewhere in the US:
- In Boston, a judge decided two Iranian nationals, university professors, should be released from detention at Logan International Airport
- An order issued in Virginia banned, for seven days, the deportation of green-card holders held at Dulles Airport and ordered the authorities to allow access to lawyers
- A Seattle judge issued an emergency stay of removal from the US for two people
The Department of Homeland Security has said it will continue to enforce the measures.
Amateur hour at the White House? – analysis by Anthony Zurcher, BBC News, Washington DC
These rulings are only the opening salvo in what will likely be a protracted legal battle, as the Trump administration forges ahead with its plans.
The episode has made the White House look amateurish and ill-prepared, however, and Republicans in Congress are getting nervous.
During the presidential primaries, a majority of Republican voters backed Mr Trump’s calls for a sweeping ban on Muslims entering the US. During the general election, he campaigned on a visa ban for certain “terrorist” countries – and won.
So it shouldn’t come as much of a surprise if the president’s core support holds firm after this weekend’s events. The views in the American heartland, far removed from major international airports, sometimes differ greatly from the liberal bastions on the coast.
However, protracted airport detention of children and the elderly is “bad optics” – and could make it harder for the White House to get public support for future immigration action.
Read more on this from Anthony
Countries react with alarm
Criticism of Mr Trump’s decision has been growing louder outside the US.
Iran is threatening a reciprocal ban on US citizens entering the country. Similar comments came out of Iraq, with whom the US is working to drive IS out of Mosul.
Chancellor Angela Merkel of Germany said “even the necessary, determined fight against terrorism does not justify placing people of a certain origin or belief under general suspicion”.
Canadian Prime Minister Justin Trudeau tweeted that his government remained committed to welcoming “those fleeing persecution, terror and war”.
A spokesperson for UK PM Theresa May said she “did not agree” with the restrictions, and French independent presidential candidate Emmanuel Macron tweeted: “I stand with the people fleeing war and persecution”.