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 : « Our country needs strong borders and extreme vetting, NOW, » while his chief of staff said only 109 people had been detained.
A number of judges ruled on the issue – one federal judge temporarily halted the deportation of visa holders.
There has been condemnation from countries around the world.
Mr Trump’s executive order , signed on Friday, halted the entire US refugee programme and also instituted a 90-day travel ban for nationals from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Those who were already mid-flight were detained on arrival – even if they held valid US visas or other immigration permits.
Thousands gathered at airports around the country to protest, including lawyers who offered their services for free to those affected.
Further demonstrations are expected on Sunday – including one outside the White House.
White House Chief of Staff Reince Priebus said that, of the 325,000 people entering the US on Saturday, 109 were detained.
« Most of those people were moved out, » he told NBC’s Meet the Press programme.
« 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 Obama administration as the most likely to harbour terrorists, and did not rule out the fact that more countries could be added to the list.
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 ».
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 in Virginia
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.
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:
But the Department of Homeland Security said it would continue to enforce the measures .
Criticism of Mr Trump’s decision has been growing louder outside the US.
Iran and Iraq are threatening a reciprocal ban on US citizens entering the country.
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 ».
