Judge James Robart ruled there were legal grounds to challenge the ban.
Mr Trump reacted furiously, calling Mr Robart`s ruling "ridiculous" and vowing to restore his ban.
People affected by the ban treated news of the suspension warily as airlines began allowing them to board flights to America on Saturday.
Judge Robart`s temporary restraining order on Friday halted the ban with immediate effect.
Since then, the state department has said it is reversing visa cancellations and US homeland security employees have been told by their department to comply with the ruling.
Customs officials told airlines that they could resume boarding banned travellers. Qatar Airways, Air France, Etihad Airways, Lufthansa and others said they would do so.
What can Trump do?
The Trump administration argues that the travel ban is designed to protect the US.
It has promised to seek "at the earliest possible time" an emergency stay that would restore the restrictions.
Meanwhile, the US president has raged against Judge Robard on Twitter.
"The opinion of this so-called judge, which essentially takes law-enforcement away from our country, is ridiculous and will be overturned!" he wrote..
"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!"
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