US President Donald Trump has vowed to overturn a legal ruling which suspended his ban on travellers from seven mainly Muslim countries.
He described federal judge James Robart as a “so-called” justice whose “ridiculous” opinion “essentially takes law-enforcement away from” the US.
Judge Robart ruled on Friday that the prohibition was unconstitutional.
A number of airlines have said they are allowing nationals targeted by the ban to board flights to America.
“The opinion of this so-called judge, which essentially takes law-enforcement away from our country, is ridiculous and will be overturned!” Mr Trump said on Twitter.
“When a country is no longer able to say who can, and who cannot , come in & out, especially for reasons of safety & security – big trouble!” he tweeted separately.
The US administration argues that his executive order last week, which caused confusion and anger, is designed to protect the US.
The ban’s implementation was halted with immediate effect by Judge Robart’s ruling in Seattle.
Customs officials told airlines that they could resume boarding banned travellers. Within hours, Qatar Airways said it would do so, followed by Air France, Etihad Airways, Lufthansa and others.
“All passengers with valid travel documents are currently eligible to board on LH flights to any US airport,” Lufthansa said.
“We will continue communicating with the US Customs and Border Protection (CBP) and will fully comply with the applicable immigration regulations.”
Iranian infant affected
Some would-be travellers were wary at news the ban had been suspended.
Ibrahim Ghaith, a Syrian barber who fled Damascus in 2013, told Reuters news agency in Jordan: “Today we heard that the measures may have been abolished but we are not sure if this is just talk. If they go back on the decision, people will be overjoyed.”
Among those expected to travel soon is an Iranian infant with a heart defect who had been due to undergo life-saving surgery in the US.
The family of four-month-old Fatemeh Reshad flew her to Dubai last week to get a visa to enter the US, but this was denied under Mr Trump’s ban.
The girl will now be allowed into the country and doctors have pledged to treat her for free, New York Governor Andrew Cuomo said late on Friday.
However it is unclear how many people concerned by the ban will decide to risk flying to the US.