The House passed the measure 289-137, in a rebuke to the White House.
President Barack Obama has said he will veto the legislation.
The bill follows the ISIS-led attacks in Paris that left 129 people dead.
Seven of the perpetrators died in the attacks, and one of them is thought to have been a Syrian who entered Europe via Greece with migrants.
The bill still needs to pass the Senate before hitting Barack Obama’s desk.
It would require the head of the FBI, the Department of Homeland Security, and the Director of National Intelligence to sign off on each refugee as being “not a threat to the security of the United States,” following an FBI background check.
Calling the Paris attacks “a game changer”, Rep Brad Ashford, a Democrat from Nebraska, said: “I cannot sit back and ignore the concerns of my constituents and the American public.”
House Majority Leader Kevin McCarthy said he supported the bill because “it is against the values of our nation and the values of a free society to give terrorists the opening they are looking for”.
Others urged compassion for those fleeing the war-torn regions.
“Defeating terrorism should not mean slamming the door in the faces of those fleeing the terrorists,” said Rep Jerrold Nadler, a Democrat from New York.
“We might as well take down the Statue of Liberty.”
Republicans do not have the votes to override Barack Obama’s veto, but say that their affirmative vote in symbolic.
Rand Paul, a senator from Kentucky who is currently running for president, has highlighted a 2011 case in his home state of two Iraqi refugees who schemed to send rifles, missiles and money to al-Qaeda against US troops in Iraqi. They are now imprisoned.
The White House has said that 2,174 Syrians have been admitted to the US since the attacks in September 2001, and noted that none of them has been arrested or deported for terror offences.
Millions of Syrians have fled to neighboring countries and to Europe since the Syrian conflict began about four years ago.
The Obama administration announced in September that it wanted to resettle about 10,000 Syrian refugees in the US by the same time in 2016.
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