REUTERS/Eric Thayer
Trump has alluded to such ideas before, but he went further Monday by writing the proposal into a major policy speech.
"A Trump administration will establish a clear principle that will govern all decisions pertaining to immigration," he said. "And we will be tough. And we will be, even, extreme. We should only admit into this country those who share our values and respect our people."
He then equated his proposed "screening test" to the Cold War.
"In the Cold War, we had an ideological screening test. The time is overdue to develop a new screening test for the threats we face today," Trump said. "I call it 'extreme vetting.' I call it extreme, extreme, vetting. Our country has enough problems. We don't need more. And these are problems like we've never had before."
Trump implied that the test would question whether immigrants want to implement Islamic law in the US, a fear commonly voiced by some conservatives.
"In addition to screening out all members or sympathizers of terrorist groups, we must also screen out any who have hostile attitudes towards our country or its principles - or who believe that Sharia law should supplant American law," he said. "Those who do not believe in our Constitution, or who support bigotry and hatred, will not be admitted for immigration into our country."
He then echoed his controversial proposal to ban foreign Muslims from entering the US. But his proposal is now aimed at those from specific regions rather than a specific religion.
"To put these new procedures in place, we will have to temporarily suspend immigration from some of the most dangerous and volatile regions of the world that have a history of exporting terrorism," he said. "As soon as I take office, I will ask the State Department and the Department of Homeland Security to identify a list of regions where adequate screening cannot take place."
Trump said there are "many such regions," but did not name them specifically.
"We will stop processing visas from those areas until such time as it is deemed safe to resume based on new circumstances or new procedures," Trump said.
Earlier in the speech, Trump cited terrorist attacks on US soil carried out by immigrants or children of immigrants as the reasoning behind the stricter immigration policies.
"The common thread linking the major Islamic terrorist attacks that have recently occurred on our soil - 9/11, the Ft. Hood shooting, the Boston Bombing, the San Bernardino attack, the Orlando attack - is that they have involved immigrants or the children of immigrants. Clearly, new screening procedures are needed."