White House staff downplayed the 300 or so travelers whom they said were stopped or detained worldwide after the sweeping executive order took effect almost immediately following Trump's Friday signing.
The measure temporarily suspends the arrival of refugees and imposes tough new controls on travelers from seven Muslim-majority countries: Iran, Iraq, Libya, Somalia, Syria, Sudan and Yemen.
White House spokesman Sean Spicer said today that out of 325,000 people arriving in the United States from foreign countries the day before, only about 100 had come from those seven nations and undergone processing.
Trump's close aide Kellyanne Conway said only around 300 people -- including those who were prevented from boarding their planes -- had been affected around the globe.
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"I think in terms of the upside being greater protection of our borders, of our people, it's a small price to pay," she said.
White House Chief of Staff Reince Priebus told CBS's "Face the Nation" that "the vast majority of the people were released."
However, "a couple dozen" remain for further questioning, he said.
Speaking on NBC's "Meet the Press" he also walked back previous White House statements about the status of individuals from the affected countries who possess green cards.
A White House official had previously said that holders of a green card -- which allows permanent residence in the US and often takes years to obtain -- who are abroad should first go to the US consulate to obtain a document allowing return to the US.
"The executive order doesn't affect green card holders moving forward," Priebus told NBC.
Customs and border control officials, "if they have a person traveling back and forth to Libya or Somalia or Yemen... Might ask a few more questions at JFK or some other airport," Priebus said.
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