Trump had promised the measures, called "extreme vetting," during last year's election campaign, saying they would prevent militants from entering the United States from abroad. But civil rights groups have condemned the order as harmful and discriminatory.
The details of the order were not immediately available but were expected to be released by the White House on Friday night.
Republican Representative Michael McCaul, the House Homeland Security Committee chairman, said on CNN that Trump's order would include a 30-day suspension of visa applications from seven countries designated as "high-threat areas" and a suspension of the refugee program.
"I'm establishing new vetting measures to keep radical Islamic terrorists out of the United States of America. Don't want them here," Trump said at the Pentagon.
"We only want to admit those into our country who will support our country and love deeply our people," he said.
The move was immediately condemned by Democrats, civil rights groups and aid groups such as Oxfam and others, even before full details emerged.
"‘Extreme vetting’ is just a euphemism for discriminating against Muslims," American Civil Liberties Union Executive Director Anthony Romero said in a statement.
"Identifying specific countries with Muslim majorities and carving out exceptions for minority religions flies in the face of the constitutional principle that bans the government from either favoring or discriminating against particular religions," Romero said.
Separately, Trump said that Syrian Christians will be given priority when it comes to applying for refugee status, a policy that would likely be challenged on similar grounds.
"If you were a Muslim you could come in, but if you were a Christian, it was almost impossible and the reason that was so unfair, everybody was persecuted in all fairness, but they were chopping off the heads of everybody but more so the Christians," Trump said in an excerpt of an interview with the Christian Broadcasting Network, discussing the Syrian refugees.
Statistics provided by the Pew Research Center last October do not support Trump's argument. Pew research found that 38,901 Muslim refugees entered the United States in fiscal year 2016 from all countries, almost the same number, 37,521, as Christian refugees.
Stephen Legomsky, a former Chief Counsel at U.S. Citizenship and Immigration Services in the Obama administration, said prioritizing Christians could be unconstitutional.
"If they are thinking about an exception for Christians, in almost any other legal context discriminating in favor of one religion and against another religion could violate the constitution," he said.
But Peter Spiro, a professor at Temple University Beasley School of Law, said Trump’s move would likely be constitutional because the president and Congress are allowed considerable deference when it comes to asylum decisions.
"It’s a completely plausible prioritization, to the extent this group is actually being persecuted," Spiro said.
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