The Justice Department's filing means the case will land back at the US 9th Circuit Court of Appeals, which upheld a halt of Trump's first travel ban before the US president revised it.
The appeal comes a day after US District Judge Derrick Watson in Hawaii dealt another blow to the White House, issuing a longer-lasting suspension of the president's travel restrictions by changing it from a temporary restraining order into a preliminary injunction.
Trump's revised travel ban aims to close US borders to nationals of Iran, Libya, Somalia, Sudan, Syria and Yemen for 90 days, and all refugees for at least 120 days.
The original executive order included Iraq but that country was removed in the rewrite.
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The Trump administration's wide-ranging initial travel restrictions imposed on January 27 were slapped down by federal courts, after sparking international protests and chaos at US airports.
Both of the bans have been criticized as amounting to a ban on entry of Muslims into the US.
The president has said his proposed travel ban is needed to preserve US national security and keep out terrorists intent on doing harm to Americans.
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