Federal Judge James Robart ruled against government lawyers’ claims that US states did not have the standing to challenge Trump’s executive order, Joinfo.com reports with reference to the BBC.
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 travellers while a legal case is heard.
Gulf carrier Qatar Airways told Reuters news agency it would start accepting all passengers with valid travel documents.
The 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 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.
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.
Dozens of lawsuits have been filed against the executive order since it was signed by Trump a week ago but this is the first time a nationwide order has been granted – temporarily voiding the president’s ban.
But the order could be reinstated once the justice department files a motion to quash the Seattle court’s ruling. In a statement the White House initially called it “outrageous”, before withdrawing that description.
The executive order caused chaos when it was suddenly introduced a week ago – some travellers arriving in the US were turned back, and protests broke out at airports across the country. The Seattle judge issued his order on the grounds that the travel ban could be unconstitutional – an argument that could be challenged all the way to the Supreme Court.
An estimated 60,000 people from the seven countries affected had their visas cancelled because of the ban. The customs department said those visas would now be reissued, and the people involved were free to travel to the US.