The court ruling dealt a further setback to Trump, who has denounced the judge in the state of Washington who blocked his Jan. 27 order on Friday. In tweets and comments to reporters, the president has insisted he will get the ban reinstated.
Trump says the temporary immigration restrictions on citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen, and on all refugees, are necessary to protect the United States from Islamist militants. Critics say they 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.
In a brief order, the 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.
The government's appeal says the decision by Judge James Robart in Washington posed an immediate harm to the public, thwarted enforcement of an executive order and "second-guesses the president's national security judgment about the quantum of risk posed by the admission of certain classes of (non-citizens) and the best means of minimizing that risk".
Trump denounced the "so-called" judge in a series of tweets on Saturday and told reporters: "We'll win. For the safety of the country, we'll win."