UPDATE 7:57am United States President Donald Trump has launched a second Twitter attack on a judge who blocked a travel ban on citizens of seven mainly Muslim nations.

“Just cannot believe a judge would put our country in such peril. If something happens blame him and court system. People pouring in. Bad!,” he tweeted on Monday morning (AEDT).

“I have instructed Homeland Security to check people coming into our country VERY CAREFULLY. The courts are making the job very difficult!”

It comes after the San Francisco-based 9th US Circuit Court of Appeals, in a brief order, denied the Trump administration’s request to set aside a Seattle judge’s ruling that put a temporary hold on the ban.

Earlier, Mr Trump vowed to reinstate his travel ban “for the safety of our country”, as visa holders affected by the executive order scrambled to board US-bound flights before the door is closed again.

Federal Judge James L Robart temporarily invalidated the ban on Friday night (local time), and on Saturday night the US Justice Department filed a formal appeal against the ruling.

However, a US appeals court on Sunday night (AEST) rejected the Trump administration’s request to immediately reinstate the travel ban, barring citizens from seven mainly Muslim countries and temporarily banning refugees.

“Appellants’ request for an immediate administrative stay pending full consideration of the emergency motion for a stay pending appeal is denied,” the ruling by the US Court of Appeals for the 9th Circuit said.

The denial of an immediate stay means the legal battles will continue for days at least.

But Mr Trump was defiant when speaking to reporters at his private Mar-a-Lago resort in Florida on Saturday. “We’ll win. For the safety of our country, we’ll win.”

He 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 judge opens up our country to potential terrorists and others that do not have our best interests at heart. Bad people are very happy!

— Donald J. Trump (@realDonaldTrump) February 5, 2017

The Justice Department said it was the “sovereign prerogative” of a president to admit or exclude immigrants, and its court appeal said the ruling “second-guesses the President’s national security judgment”.

It argued that the President acted within his constitutional authority and blocking the order “immediately harms the public by thwarting enforcement of an executive order issued by the President, based on his national security judgment”.

Small numbers of travellers from the previously banned countries began making trips to the United States in the knowledge that Judge Robart’s ruling could be overturned at any time, the New York Times reported.

After the State Department reversed its cancellation of visas for people from the seven affected countries – Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen – aid groups scrambled to take advantage of the window for refugees to enter the United States.

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.

Ali Vayeghan (R) arrives in Los Angeles after previously being barred entry to the US. Photo: Getty

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.”

Meanwhile, about 3000 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.

A flag-draped coffin which protesters said symbolised the death of democracy is carried to Mar-a-Lago Resort. Photo: Getty

Who is Judge Robart?

Judge Robart was appointed by President George W. Bush and is known for his conservative views.

In reversing the ban, he declared in his ruling that “there’s no support” for the Trump administration’s argument that “we have to protect the U.S. from individuals” from the affected countries.

Judge Robart is known for his conservative views. Photo: AP

Jonathan Turley, a law professor at George Washington University, said Mr Trump’s criticism of Judge 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.”

– with ABC and AAP