Republican leaders on Capitol Hill called on Tuesday for a “pause” in admitting Syrian refugees to the United States, citing national security risks in the wake of the Paris attacks.

Fears of a domestic terrorist infiltration have suffused the congressional reaction to Friday’s attacks, and there were indications those fears could bleed into coming negotiations over funding the federal government.

According to the most recent State Department figures, 1,600 Syrian refugees have been admitted to the U.S. since the Syrian civil war began in 2011, and President Obama committed in September to accepting 10,000 more over the next year.

But Republicans said threats from Islamic State radicals demand at least a temporary halt to the program until the vetting process can be assured.

“Our nation has always been welcoming, but we cannot let terrorists take advantage of our compassion,” House Speaker Paul D. Ryan (R-Wis.) said Tuesday. “This is a moment where it’s better to be safe than to be sorry.”

Senate Majority Leader Mitch McConnell (R-Ky.) also said on Tuesday that he backs a “pause or a moratorium” on allowing Syrian refugees into the county.

“Compassion for those refugees is important,” Sen. John Cornyn (R-Tex.), the majority whip, said in remarks Tuesday on the Senate floor. “But protecting our homeland and keeping the American people safe is the first order of business.”

House leaders indicated they intend to bring refugee legislation to a floor vote before the end of the week, but there appeared to been less enthusiasm for a stand-alone bill in the Senate, where lawmakers appeared to be trained on the upcoming spending bill.

Appropriators are currently negotiating a bill to fund the federal government through next September before the current spending authority expires on Dec. 11. A policy “rider” on that bill could constrain the Obama administration’s resettlement efforts.

Democrats on Capitol Hill approached the issue carefully on Tuesday, with most saying a balance could be drawn between maintaining U.S. national security and addressing the humanitarian crisis in Europe and the Middle East.

Senate Minority Leader Harry M. Reid (D-Nev.) noted that the existing refugee vetting process takes an average of 18 to 24 months and that senators would be briefed on that process by administration officials on Wednesday:”I don’t think at this stage we should be pausing until we get the facts,” he said.

But another Democratic leader, Sen. Charles E. Schumer (N.Y.), said “a pause may be necessary.”

“We have to see how good the process is,” he said. “And if it has holes in it, and it doesn’t work, we will tighten it up.”

Across the Capitol, Ryan tapped House Majority Leader Kevin McCarthy (R-Calif.) to lead a task force of six committee chairmen to look at ways for Congress to address both the refugee crisis and the battle against the Islamic State, which claimed responsibility for Friday’s attacks in Paris.

Lawmakers had already started floating legislation of their own. Rep. Raul Labrador (R-Idaho) said he will introduce a bill that will strip the president of authority to raise the legal cap on refugees, for instance, while Rep. Richard Hudson (R-N.C.) introduced a bill creating new vetting standards.

In a vivid sign of the political potency of the issue, Sen. David Vitter (R-La.) flew back to Washington, just days before he will stand for election in a closely fought governor race, to introduce a bill Tuesday to bar Syrian refugees.

The task force appeared Tuesday to move toward Hudson’s approach, which would require the Department of Homeland Security to certify that each refugee admitted from Syria or Iraq do not pose a security threat and to require an FBI background checks for those refugees. The bill would also require the DHS inspector general to audit those certifications.

But some Republican lawmakers said they want a broader halt to the flow of refugees coming into the United States, arguing that potential terrorists and terrorist sympathizers could come from places besides Syria and Iraq.

But Ryan said the pause he was advocating would be limited in scope: “It’s important that we have a refugee system in place. We respect that. But we think it’s simply prudent that for this particular program in this particular situation that we be better guarded against any possible infiltration.”

Republican leaders, aware that stand-alone legislation may not make it into law, left the door open to adding refugee language to the year-end spending bill — an approach that is likely to have the strong backing of conservatives.

“Holding the money is the best,” said Rep. Lou Barletta (R-Pa.), who wants not only a moratorium on Syrian refugee arrivals but also a reexamination of the overall visa waiver program that allows visitors from 38 countries — including France, where several of the alleged Paris attackers were legal residents — to enter the U.S. without special vetting.

But using the omnibus spending bill could run into opposition among Senate lawmakers of both parties who are eager to avoid another potential government shutdown fight.

“I don’t want to shutdown the government,” said Senate Armed Services Committee Chairman John McCain (R-Ariz.). “Shouldn’t we be able to sit down and agree on something without threatening to shutdown the government for God’s sake?”

“Yet another reason to shut down the government,” said Rep. Jan Schakowsky (D-Ill.). “Let’s see, we had Planned Parenthood, Obamacare — and now let’s have refugees.”

A previous version of this story mistakenly referred to Reid as the Senate majority leader. He is the Senate minority leader.

Paul Kane contributed to this story.

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