The move seeks to reverse February 3 ruling by a federal judge in Washington.
Visa holders from the affected nations have been scrambling to get flights to the United States, fearing they have a slim window to enter America.
Donald Trump’s ban last week led to mass protests and confusion at US airports.
Some 60,000 visas have been revoked since President Trump’s executive order was issued.
However, Judge James Robart’s temporary restraining order halted it nationwide with immediate effect.
Judge Robart found that legal challenges launched by two states, Washington and Minnesota, were likely to succeed.
State lawyers had argued that the ban was unconstitutional because it denied people with valid entry documents the right to travel without due process.
It also violated freedom of religion rights by appearing to target Muslims, they said.
Donald Trump called Judge James 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 executive order also suspends the US Refugee Admissions Program for 120 days, and places an indefinite ban on Syrian refugees.
The appeal against the suspension was formally filed by the Department of Justice on February 4.
Donald 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, President Trump took to Twitter to rage against Judge James Robart, who has served on the federal bench since 2004 after nomination by President George W. Bush.
He tweeted: “The opinion of this so-called judge, which essentially takes law-enforcement away from our country, is ridiculous and will be overturned!”
Donald 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.?”
He later predicted that the appeal would succeed.
“We’ll win. For the safety of the country, we’ll win,” Donald Trump told reporters.
The state department has said it is reversing visa cancelations and US homeland security employees have been told by their department to comply with the ruling.
Customs officials told airlines that they could resume boarding banned travelers. Qatar Airways, Air France, Etihad Airways, Lufthansa and others said they would do so.
Travelers from the affected countries have been trying to use the window of opportunity by boarding US-bound flights on February 4.
However, there were also reports that a number of travelers were not allowed to fly to America.
In Djibouti, east Africa, immigrants from all seven countries on the list were not allowed to fly, an immigration attorney was quoted as saying by AP.
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