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The US Justice Department appealed a temporary block of Donald Trump's travel ban on citizens from seven mainly Muslim countries on Saturday, after the president unleashed a fiery tirade and those with valid visas started arriving on American soil.

It was just the latest in a series of dramatic twists since the Republican billionaire leader issued his immigration order a week ago.

The Justice Department filed its motion to appeal, though the legal brief detailing its arguments has yet to come, and the case will now move to a federal appeals court.

"We'll win. For the safety of the country, we'll win," Trump told reporters.

US authorities suspended President Donald Trump's controversial ban on travellers from seven Muslim-majority countries, following a court ruling that blocked its enforcement on Saturday.

"We have reversed the provisional revocation of visas," a US State Department spokesman told AFP.

The department had said some 60,000 travel visas had been revoked in compliance with the president's recent executive order.

"Those individuals with visas that were not physically cancelled may now travel if the visa is otherwise valid," the official said.

The official added that the Trump administration is "working closely with the Department of Homeland Security and our legal teams" pending a full review of a complaint filed by Washington state's attorney general, which filed one of several legal challenges to the measure.

Trump lashed out at a court ruling on Saturday, dismissing it as "ridiculous" and vowing to get it overturned.

The travel restrictions, which went into effect a week ago, have wreaked havoc at airports across America, sparked numerous protests and left countless people hoping to reach the United States in limbo.

"The opinion of this so-called judge, which essentially takes law-enforcement away from our country, is ridiculous and will be overturned!" Trump wrote in a familiar flurry of early morning tweets.

"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!" Trump wrote, less than 12 hours after the ruling was issued in Seattle.

Trump was forced to defend a botched rollout of the plan - which called his government's competence into question - and fired the acting attorney general for refusing to defend the order in court.

His approval rating has sunk to the lowest level on record for any new president.

His latest rhetorical outburst is only likely to stoke the controversy.

Presidents from Thomas Jefferson to Barack Obama have criticised court rulings, but have rarely, if ever, criticised individual judges.

"I can't think of anything like it in the past century and a half at least," constitutional scholar and Harvard Law professor Laurence Tribe told AFP.

"It's not exactly contempt of court, but it certainly is contemptuous," said Tribe, who taught two sitting Supreme Court justices as well as Obama - whom he later advised.

"It conveys a lack of respect for the independent judiciary that bodes ill for the country's future as long as Trump occupies the presidency," Tribe said.