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. In tweets and comments to reporters, the president has insisted he will get the ban reinstated.
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. Critics say the measures are unjustified and discriminatory.
The judge's order and the appeal ruling have created what may be a short-lived opportunity for travelers 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 U.S. citizen, who boarded a plane from Cairo to Turkey on Sunday to connect with a U.S.-bound flight. She declined to be named for fear it could complicate her entry to the United States.
In a brief order, the U.S. 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.
Reacting to the court's statement, Iraqi government spokesman Saad al-Hadithi said: "It is a move in the right direction to solve the problems that it caused."
"WHAT IS OUR COUNTRY COMING TO?"
Trump's Jan. 27 travel restrictions have drawn protests in the United States, provoked criticism from U.S. 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 Sept. 11, 2001 attacks on the United States as a justification for the ban, saying no attacks had been carried out on U.S. 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".
The 9/11 attacks were carried out by hijackers from Saudi Arabia, the United Arab Emirates, Egypt and Lebanon, whose nationals were not affected by the order.
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 U.S.?" he asked.
Trump told reporters at his private Mar-a-Lago resort in Florida: "We'll win. For the safety of the country we'll win."
But the Washington court ruling was the first move in what could be months of legal challenges to his push to clamp down on immigration.
The Justice Department appeal criticized Robart's legal reasoning, saying it violated the separation of powers and stepped on the president's authority as commander-in-chief.
The appeal said the state of Washington lacked standing to challenge the order and denied that the order "favors Christians at the expense of Muslims."
The U.S. 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 thegovernment said it expects to begin admitting refugees again onMonday.
Iraqi Fuad Sharef, his wife and three children spent two years obtaining U.S. visas. They had packed up to move to America last week, but were turned back to Iraq after a failed attempt to board a U.S.-bound flight from Cairo.
On Sunday, the family checked in for a Turkish Airlines flight to New York from Istanbul.
"Yeah, we are very excited. We are very happy," Sharef told Reuters TV. "Finally, we have been cleared. We are allowed to enter the United States."
Rana Shamasha, 32, an Iraqi refugee in Lebanon, was due to travel to the United States with her two sisters and mother on Feb. 1 to join relatives in Detroit until their trip was canceled as a result of the travel ban.
She is now waiting to hear from U.N. officials overseeing their case. "If they tell me there is a plane tomorrow morning, I will go. If they tell me there is one in an hour, I will go," she told Reuters by telephone in Beirut, saying their bags were still packed. "I no longer have a house here, work, or anything," she said.
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 U.S.-bound flights since Saturday.
Banner and thumbnail credit: Reuters, Ringo Chiu