Trump Appeal Against Seattle Judge's Travel Ban Ruling
The move seeks to reverse Friday's ruling by a federal judge in Washington state.
Visa holders from the affected nations have been scrambling to get flights to the US, fearing they have a slim window to enter America.
Mr Trump's ban last week led to mass protests and confusion at US airports.
There were further demonstrations on Saturday in Washington, Miami and other US cities as well as in a number of European capitals.
Thousands of people turned out in London, with smaller protests in Paris, Berlin, Stockholm and Barcelona.
Trump supporters staged some counter-protests in the US.
Some 60,000 visas have been revoked since Mr Trump's executive order was issued.
But Judge James Robart's temporary restraining order halted it nationwide with immediate effect.
He found that legal challenges launched by two states, Washington and Minnesota, were likely to succeed.
Mr Trump called Judge Robart's ruling "ridiculous", vowing to restore the ban.
The ban envisages a 90-day visa suspension for anyone arriving from Iraq, Syria, Iran, Libya, Somalia, Sudan and Yemen.
The directive also suspends the US Refugee Admissions Programme for 120 days, and places an indefinite ban on Syrian refugees.
The appeal against the suspension was formally filed by the US Department of Justice on Saturday.
Mr Trump is named as one of the appellants in his capacity as president, along with Homeland Security Secretary John Kelly and Secretary of State Rex Tillerson.
The administration argues that the travel ban is designed to protect the US, and it is seeking an emergency stay that would restore the restrictions.
Meanwhile, the US president raged against Judge Robart in a series of tweets.
"The opinion of this so-called judge, which essentially takes law-enforcement away from our country, is ridiculous and will be overturned!" he wrote.
Mr Trump later added in another tweet: "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.?"
The president later predicted that the appeal would succeed.
"We'll win. For the safety of the country, we'll win," he told reporters.