The order singled out Syrians for the most aggressive ban, indefinitely blocking entry for anyone from that country, including those fleeing civil war.
The order sparked protests at several United States airports, including New York's Kennedy and Chicago's O'Hare and those in Minneapolis and Dallas-Forth Worth.
An official said Afghanistan, Malaysia, Pakistan, Oman Tunisia and Turkey were Muslim-majority countries not included in the order.
"The order is not affecting green card holders moving forward", Trump's chief of staff, Reince Priebus, announced on Meet the Press yesterday.
Priebus says officials were using "discretionary authority" to ask "a few more questions" at US airports.
President Donald Trump's administration says green card holders - including those detained at airports across the United States in the wake of Trump's ban on travel from seven nations - will be allowed into the country.More news: FedEx issues statement on Iowa City flag burning incident
Those already in the USA with a visa or green card would be allowed to stay, according to the homeland security official. "We're off on a tangent that has nothing to do with the executive order".
But a federal judge in NY temporarily blocked part of Trump's order late on Saturday night, ruling that citizens of the seven countries who hold valid visas and have already arrived in the United States can not be removed from the United States.
"The entry of these individuals, subject to national security checks, is in the national interest". President Trump had made.
The statement, which did little to clear up the confusion and frustration playing out at airports across the globe, said the administration "will comply with judicial orders" even as it continues to carry out the president's order.
Trump administration officials have given different messages on who the order would affect. People with work visas or dual citizenship are among those being screened at airports. "Since the terrorist attacks of September 11, 2001", the Times notes, citing University of North Carolina sociologist Charles Kurzman, "no one has been killed in the United States in a terrorist attack by anyone who emigrated from or whose parents emigrated from Syria, Iraq, Iran, Libya, Somalia, Sudan and Yemen".More news: Understanding Trump Press Secretary Sean Spicer
The official said that as of midday Sunday, 170 people had applied for and been granted the waivers, and stressed that only a fraction of all the travelers to the United States since Trump signed his order on Friday were affected. And if they're folks that shouldn't be in this country they're going to be detained.
Someone save us. going forward.
"Banning travelers from seven Muslim countries to the U.S. is tantamount to provide fuel to extremism".
The US support, she said, could also be handy in resolving other issues with India and defusing tensions in South Asia.
Mrs Merkel and Mr Trump spoke by phone on Saturday for the first time since his inauguration.More news: President Donald Trump Mocks Chuck Schumer for 'Fake Tears'