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.
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 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.
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 expected on Sunday – including one outside the White House.
