US President Donald Trump has vowed to reinstate his controversial travel ban "for the safety of our country", as visa holders affected by the action scramble to board US-bound flights, fearing they only have a short window to enter the country.

Key points: Justice Department to fight federal judge's ruling that travel ban be lifted

Justice Department to fight federal judge's ruling that travel ban be lifted Donald Trump slams "ridiculous" ruling by "so-called judge"

Donald Trump slams "ridiculous" ruling by "so-called judge" Travellers affected by ban scramble to enter US

Travellers affected by ban scramble to enter US Who is the judge who blocked the ruling?

A federal judge temporarily invalidated the ban on Friday night (local time), and the US Justice Department today filed a formal appeal against the ruling.

"We'll win. For the safety of our country, we'll win," Mr Trump told reporters at his private Mar-a-Lago resort in Florida.

Mr Trump had earlier called the ruling by the "so-called judge" ridiculous.

"Because the ban was lifted by a judge, many very bad and dangerous people may be pouring into our country. A terrible decision," he tweeted.

The Justice Department said it was the "sovereign prerogative" of a president to admit or exclude immigrants, and its appeal cited a "basic principle that an alien seeking initial admission to the United States requests a privilege and has no constitutional rights regarding his application".

Jonathan Turley, a law professor at George Washington University, said Mr Trump's criticism of Judge James L Robart's decision could make it tougher for Justice Department attorneys as they seek to defend the executive order.

Mr Turley said presidents were usually circumspect about commenting on government litigation.

"It's hard for the President to demand that courts respect his inherent authority when he is disrespecting the inherent authority of the judiciary," he said.

"That certainly tends to poison the well for litigation."

In an interview with ABC America scheduled to air on Sunday (local time), Vice-President Mike Pence said he did not think that Mr Trump's criticisms of the judge undermined the separation of powers.

"I think the American people are very accustomed to this president speaking his mind and speaking very straight with them," Mr Pence said, according to an excerpt of the interview.

'Get on the quickest flight ASAP'

Lawyers volunteered their services at airports as international travellers began to arrive. ( Reuters: Laura Buckman )

The ban suspended America's refugee program and halted immigration to the US from seven Muslim-majority countries that the Government said raised terrorism concerns.

Amid uncertainty over whether the Justice Department would be granted an emergency freeze of the judge's order, people with pre-approved visas who could travel immediately were being urged to do so.

Rula Aoun, director of the Arab American Civil Rights League in Dearborn, Michigan, was advising people to hurry.

"We're telling them to get on the quickest flight ASAP," said Ms Aoun, whose group filed a lawsuit on Tuesday in federal court in Detroit asking a judge to declare Mr Trump's immigration order unconstitutional.

Ms Aoun said some people had to make hard choices, including a Yemeni family expected to arrive at John F Kennedy International Airport on Sunday from Egypt without two of their children.

The father and two of the children are US citizens, the mother has an immigrant visa, but the other two children did not yet have theirs and were left behind with relatives.

"They just don't want to take a chance of waiting," she said.

Meanwhile, the US State Department has moved to begin admitting refugees, including Syrians, as soon as Monday.

An email from the State Department's refugee office said the US Government was working with its legal team and interagency and overseas partners to comply with the ruling, with an official saying "expect some refugees to arrive Monday".

"We are focusing on booking refugee travel through February 17," the email said.

"We are asking that arrivals resume this Monday, the first normal travel day of the week, if possible. We are aware that some refugees may not be ready to depart on short notice."

Confusion during the rollout of the ban initially found green card holders caught in travel limbo, until the White House on Wednesday clarified that they would be allowed to enter and leave the US as they please.

Protesters converge on Trump's properties

The ban sparked protests around America, including this one in West Palm Beach. ( AP: Michael Ares )

Meanwhile, about 3,000 demonstrators marched near Mr Trump's Florida estate to protest against the now-blocked executive order.

The Saturday protest began with a rally outside Trump Plaza, twin 30-storey waterfront condo buildings in West Palm Beach.

The march headed 3.2 kilometres to Mr Trump's Mar-a-Lago resort, where the International Red Cross is holding a fundraiser.

Protesters shouted anti-Trump slogans and set up a flag-draped coffin that they said represented the death of democracy.

ABC/wires