A House task force released a bill Tuesday directed at the vetting of refugees from Syria and Iraq, where Islamic State extremists have found safe havens.  While Speaker Paul D. Ryan and Senate Majority Leader Mitch McConnell called for a halt to the refugee program, the House legislation instead seeks to enhance the certification process for these refugees.

The rush to block the resettlement of migrants fleeing a long-running civil war has sparked a heated debate on Capitol Hill about striking a balance between showing compassion and ensuring terrorist attacks such as those in the French capital on Nov. 13 will not happen on American soil. Driving some concerns is the Syrian passport found among one of the Islamic State attackers in Paris.

“We have a refugee situation that we think requires a pause and a more comprehensive assessment on how to guarantee members of ISIS are not infiltrating themselves among the refugee population,” Ryan said Tuesday after the weekly closed-door GOP conference meeting.

After a classified briefing with top administration officials, some lawmakers said their concerns about how refugees are screened have not abated.

“What I heard today reinforced every preconceived notion I had going into it, that the vetting process we have is not complete,” said Rep. Richard Hudson, R-N.C.  “And bringing these 10,000 in now does pose a grave risk that terrorists could exploit.”

Rep. Adam B. Schiff of California, the ranking Democrat on the Intelligence Committee, expressed doubt about the legislative proposal being pushed by Republicans.

“Anything constructive will be welcomed but I think there would be a lot of resistance among Democrats” to any bill that would “close the door to mothers and children.”

During the weekly House GOP conference meeting, Majority Leader Kevin McCarthy announced he would lead a task force to develop short- and long-term legislative recommendations to curb acts of terrorism and to address the influx Syrian refugees.

Ryan’s mandate was that the task force’s efforts should not be entirely focused on refugees. He said it should include a comprehensive plan to defeat the terrorist grou known as ISIS or ISIL, and suggested the legislative response would not be part of an omnibus spending bill needed to fund the government past Dec. 11.

The task force includes the following committee chairmen: Reps. Michael McCaul of Homeland Security, Mac Thornberry of Armed Services, Robert W. Goodlatte of Judiciary, Devin Nunes of Intelligence, Ed Royce of Foreign Affairs and Harold Rogers of Appropriations.

According to a McCarthy aide, the task force discussed a process under which the Department of Homeland Security — with the concurrence of the FBI director and the director of National Intelligence — would have to verify each refugee from Iraq and Syria is not a security threat before allowing them to enter the country.

The FBI would be required to conduct background checks on the refugees and the DHS inspector general would need to annually provide a risk assessment to Congress, the aide said.

Currently, the State Department is the lead agency for screening refugees. It receives referrals from the U.N. High Commissioner for Refugees and then shares them with the DHS and the Department of Health and Human Services. The FBI and Department of Defense run refugee names through various terrorism and crime databases.

Nunes, a California Republican, said the legislation is “very short and simple and puts a new vetting process in place just so we can be sure that we know what we’re dealing with.”

Although the measure does not go as far as many members wanted, Nunes said he expects it to have enough support to pass. The Judiciary Committee is looking at a longer, more comprehensive fix, he said.

Senate Minority Leader Harry Reid, D-Nev., and other top leaders reserved judgment on the refugee issue until after the chamber’s classified briefing Wednesday. Minority Whip Richard J. Durbin, D-Ill., noted thousands of refugees and millions of visitors already come into the U.S. from overseas.

“Let’s ask the hard questions about how we make sure that none of them can come into the United States and cause problems for us or any threat to our safety,” Durbin said.

Senate Intelligence Committee leaders leaving a closed meeting Tuesday afternoon expressed broader concerns, including about the availability of visas for more routine travel.

Chairman Richard M. Burr, R-N.C., and ranking Democrat Dianne Feinstein also said the committee would find ways to address new encrypted communication. Burr said it was “likely” those responsible for the Paris attacks used such encrypted communications because of the lack of chatter.

“The reality is that we don’t expect this to be received extremely well from the companies that market their product based on the fact that they have end-to-end encryption. We don’t have a responsibility to sell their products,” Burr said. “We have a responsibility to keep America safe.”

Emma Dumain, Matthew Fleming and Rachel Oswald contributed to this report.