The federal judge ruled against government lawyers’ claims that US states did not have the standing to challenge Donald Trump’s executive order.
Last week’s order has led to protests and confusion at US airports.
Customs officials have told US airlines that they can resume boarding banned travelers while a legal case is heard.
Gulf carrier Qatar Airways told Reuters it would start accepting all passengers with valid travel documents.
Trump administration, however, could again block them if it were to win an emergency stay. The justice department says it will appeal against the Seattle ruling.
In a statement, the White House described Donald Trump’s directive as “lawful and appropriate”.
“The president’s order is intended to protect the homeland and he has the constitutional authority and responsibility to protect the American people,” the statement said.
President Trump’s order suspended the US Refugee Admissions Program for 120 days.
There is also an indefinite ban on Syrian refugees. Anyone arriving from Iraq, Syria, Iran, Libya, Somalia, Sudan or Yemen faces a 90-day visa suspension.
The lawsuit against Donald Trump’s ban was initially filed by Washington State, with Minnesota joining later.
Washington state Attorney General Bob Ferguson described the ban as unconstitutional.
Donald Trump has argued that his directive is aimed at protecting America. Critics respond by saying that most terror attacks in the US in recent years have been carried out by home-grown militants.
He said visas would once again be issued once “the most secure policies” were in place, and denied it was a ban on Muslims.
Courts in at least four other states – Virginia, New York, Massachusetts and Michigan – are hearing cases challenging President Trump’s executive order.
On February 3, a judge in Boston declined to extend a temporary ban that prohibited the detention or removal of foreigners legally authorized to come to America.
The ban – which only applied to Massachusetts – is due to expire on February 5.
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