The official said the administration plans to defend the order on its merits before a federal district court instead.
Later Friday, White House spokesman Sean Spicer told NBC News that "every option is on the table," including taking the case to the Supreme Court.
Trump's executive order restricted travel for foreign nationals from seven majority-Muslim countries.
Last week, U.S. Judge James Robart issued a temporary restraining order, shelving enforcement of the president's executive action. On Thursday, the Trump administration was dealt a setback when a panel of three judges unanimously upheld a suspension of the action in a federal appeals court.
After the Thursday ruling, Trump told NBC it was a "political decision," echoing comments he made at a law enforcement conference earlier this week. The president expressed confidence that his administration would ultimately win this legal fight.
This story is developing. Please check back for further updates.