The stand-down, a day after a federal judge in Washington state temporarily blocked the ban, marked an extraordinary setback for the White House.
Only a week ago, the president had acted to suspend America's refugee program and halt immigration to the US from seven Muslim-majority countries that the government said raise terrorism concerns.
As the White House worked to reinstate the ban, Trump mocked US District Judge James Robart, appointed by President George W Bush, as a "so-called judge" whose "ridiculous" ruling "will be overturned."
Trump's direct attack recalled his diatribes during the campaign against a federal judge of Mexican heritage who was overseeing a Trump University case.
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Justice Department lawyers could be called upon to answer for his words as the travel ban case reaches the 9th US Circuit Court of Appeals.
The order had caused unending confusion for many foreigners trying to reach the United States, prompted protests across the United States and led to multiple court challenges.
Robart's ruling, which the White House said the Justice Department would challenge, led federal agencies to unwind enforcement of Trump's executive order. Justice filed notice Saturday it would appeal the ruling.
The State Department, after initially saying that as many as 60,000 foreigners from Iraq, Syria, Iran, Sudan, Libya, Somalia or Yemen had their visas canceled, reversed course on Saturday and said they could travel to the US if they had a valid visa.
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