"You have to prove it. How are they proving it?" Trump said at a press conference here. "I have a real concern that the people who are coming into this country are coming in, some for very bad purposes."
The New York real estate mogul's comments came on the heels of a series of coordinated terrorist attacks in Paris last week that killed more than 120 people and which ISIS has claimed responsibility for. In the aftermath of the horrific events, some Republican presidential candidates have toughened their rhetoric and raised alarm about Syrian refugees seeking to enter the United States.
Some of Trump's rivals have suggested that the country should selectively accept Christian Syrians. Allowing tens of thousands of Syrian Muslims into the country was "nothing short of lunacy," said Texas Sen. Ted Cruz, adding that it's a "different situation" altogether with Middle Eastern Christians.
Jeb Bush, meanwhile, said the country should take in "people like orphans and people who are clearly not going to be terrorists. Or Christians
Trump told reporters Wednesday that he would have had no problem taking Jewish refugees fleeing the Holocaust during World War II because they wouldn't be terrorists.
"They weren't gonna knock down the World Trade Center. They weren't gonna do damage. They weren't gonna do what happened in Paris. Much different story," Trump said.
Trump, who has not held a press conference in several weeks, answered a wide range of questions from reporters before taking the stage at a campaign rally here Wednesday. The majority of questions centered on national security and foreign policy issues, as news coverage continues to focus on last week's massacre that jolted Paris.
Trump reiterated his controversial statement that he would consider closing down mosques, calling it "common sense."
"There's tremendous hatred," he said. "Radical Islamic terrorism is a fact. ... It's a very gruesome fact. It's a very, very serious problem."
Asked whether he would consider putting American troops in Syria, he answered: "If need be, yeah."
"We've gotta get rid of ISIS quickly," he said, before adding that his preference would be for other countries to send military personnel to Syria.
"We'll back them up a 100 percent and we'll bomb the hell out of them."