A US judge has issued a temporary halt to the deportation of visa holders or refugees stranded at airports following President Trump's executive order.
The American Civil Liberties Union (ACLU) filed a case in response to the order issued on Friday.
The ACLU estimates that between 100 and 200 people are being detained at airports or in transit.
Thousands of people have been protesting at US airports over Mr Trump's clampdown on immigration.
His executive order 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.
On Saturday, Mr Trump told reporters: "It's working out very nicely. You see it at the airports, you see it all over."
Other executive orders issued by Mr Trump on Saturday were:
The ruling, from federal Judge Ann Donnelly, in New York, prevented 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.
Her ruling is not on the constitutionality of Mr Trump's executive order. What will happen to those still held at airports remains unclear.
"The feeling of injustice is so big, and this ban is so demeaning! Shame!" – Syrian scientist working on skin cancer research and living in Germany who now finds she cannot travel to Philadelphia in February to visit colleagues.
"Dreams shattered" – cardiology fellow from Jordan whose Syrian wife's family cannot come to visit in the US.
"We may try our chances with other countries" – Iranian professional in Washington DC, whose wife is now stuck in Iran.
Early on Sunday, the Department of Homeland Security said it would comply with judicial rulings but would continue to enforce Mr Trump's order.
The case was brought early on Saturday on behalf of two Iraqi men detained at JFK Airport in New York.
One worked for the US military in Iraq. The other is married to a former US military contract employee.
Both have now been released. Another court hearing is set for February.
Lee Gelernt, deputy legal director of the Immigrants Rights Project, who argued the case in court said that some people had been threatened with being "put back on a plane" later on Saturday.
Mr Gelernt also said the judge had ordered the government to provide a list of names of those detained under the order.
Judges elsewhere in the US have also ruled on the issue:
In addition to those detained on arrival in the US, some air passengers were prevented from boarding US-bound flights after the order was signed.
On Saturday five Iraqi passengers and a Yemeni national were prevented from boarding a flight at Cairo airport bound for New York.
Dutch airline KLM said it had turned away seven people who were booked on US-bound flights because they would no longer have been accepted
The restriction applies to dual nationals – so, for example, a British citizen who is also a citizen of Iran would not be able to enter the US.