House Republicans renewed their call Friday for swift Senate action on a bill cracking down on Syrian and Iraqi refugees, following the arrests of two Iraqi-born men on terrorism-related charges.

House Majority Leader Kevin McCarthy, R-Calif., released a statement urging a vote on legislation that passed the House in November after the terrorist attacks in Paris. The bill would require new FBI background checks and other steps before any refugee could come to the U.S. from Iraq or Syria, where the Islamic State group has flourished.

The bill passed with bipartisan support but was strongly opposed by the White House, which pointed out that the Syrian and Iraqi refugee program is already very limited and tightly controlled.

Senate Majority Leader Mitch McConnell, R-Ky., has pledged action on the issue in the first quarter of the year. But he hasn't specified whether he will bring up the House bill, which Minority Leader Harry Reid, D-Nev., has insisted won't pass the Senate.

McConnell has endorsed a "pause" in Syrian refugees coming to the U.S. but has moved cautiously on the issue. Despite demands from some conservatives, the Syrian refugee bill was omitted from a year-end catch-all bill in December. Instead, a more modest and broadly supported measure was included that tightened controls on the "visa waiver" program that allows visitors from 38 friendly countries to come to the U.S. without visas.

McConnell's spokesman, Donald Stewart, said Friday that McConnell's position hasn't changed.

But he faces new pressures from fellow Republicans in the House as well as those running for president. Sen. Ted Cruz of Texas called immediately for a retroactive review of all refugees who have come to the U.S.

Authorities alleged that one of the men arrested Thursday traveled to Syria to fight with terrorists in the civil war and the other provided support to the Islamic State group. There was no evidence either man — one from Texas and the other from California — intended or planned attacks in the United States.

Rep. Michael McCaul, R-Texas, chairman of House Homeland Security Committee, held a press conference with other lawmakers to step up pressure on the Senate.

"This is an issue of safety to the American people," McCaul said. If the latest arrests are not enough evidence as to why we need this legislation passed, "I don't know what more is necessary," he said.

Rep. Buddy Carter, R-Ga., said the "the vetting system needs to be improved." The House has acted, and "now it's time for the Senate to do their part," Carter said.


Associated Press writer Matthew Daly contributed to this report.