The Trump administration is standing firm over its ban on immigration from seven countries despite court rulings and mass protests against it.
In a statement, President Trump said visas would once again be issued once “the most secure policies” were in place, and denied it was a Muslim ban.
The move has been widely condemned.
Sixteen state attorneys general have said the order is unconstitutional. Several federal judges have temporarily halted the deportation of visa holders.
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.
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 were held on Sunday, including protests outside the White House and Trump Tower in New York.