A US appeal court late denied a request from the Department of Justice to immediately restore an immigration order from President Donald Trump barring citizens from seven mainly Muslim countries and temporarily banning refugees.

The court ruling dealt a further setback to Trump, who has denounced the judge in the state of Washington who blocked his executive order on Friday.

Trump says the 90-day travel ban on citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen, and a 120-day bar on all refugees, are necessary to protect the United States from Islamist militants.

The judge's order and the appeal ruling have created what may be a short-lived opportunity for travellers from the seven affected countries to get into the United States while the legal uncertainty continues.

"This is the first time I try to travel to America. We were booked to travel next week but decided to bring it forward after we heard," said a Yemeni woman, recently married to a US citizen, who boarded a plane from Cairo to Turkey on Sunday to connect with a US-bound flight.

She declined to be named for fear it could complicate her entry to the United States.

In a brief order, the US appeals court said the government's request for an immediate administrative stay on the Washington judge's decision had been denied.

It was awaiting further submissions from Washington and Minnesota states on Sunday, and from the government on Monday.

Iraqi government spokesman Saad al-Hadithi believed the move was the right one.

"It is a move in the right direction to solve the problems that it caused," al- Haditihi said.

Trump's travel restrictions have drawn protests in the United States, provoked criticism from US allies and created chaos for thousands of people who have, in some cases, spent years seeking asylum.

In his ruling in Washington state on Friday, Judge James Robart questioned the use of the September 11, 2001 attacks on the United States as a justification for the ban, saying no attacks had been carried out on US soil by individuals from the seven affected countries since then.

For Trump's order to be constitutional, Robart said, it had to be "based in fact, as opposed to fiction".

In a series of tweets on Saturday, Trump attacked "the opinion of this so-called judge" as ridiculous.

"What is our country coming to when a judge can halt a Homeland Security travel ban and anyone, even with bad intentions, can come into US?" Trump asked.

The Justice Department appeal criticised Robart's legal reasoning, saying it violated the separation of powers and stepped on the president's authority as commander-in-chief.

The US State Department and Department of Homeland Security said they were complying with Robart's order and many visitors are expected to start arriving on Sunday, while the government said it expects to begin admitting refugees again on Monday.

An official at Beirut airport said three Syrian families had left for the United States via Europe on Sunday morning.

Airline sources in Cairo said that 33 people from the seven affected countries had been allowed to board US-bound flights since Saturday.