Sen. Ted Cruz, R-Texas, has introduced legislation to bar refugees from any country “substantially controlled” by a terrorist group from entering the United States.

“After watching the horrific scenes play out in Paris, we have to take basic steps to protect ourselves from the growing threat of radical Islamic terrorism,” Cruz said in a statement. “This legislation will do just that.”

In the wake of the Paris terrorist attacks Nov. 13, Cruz’s bill becomes part of the debate over President Obama’s promise to accept at least 10,000 Syrian refugees in the next year.

After a Syrian passport was discovered near the body of one of the Paris attackers,  Democrat and Republican lawmakers have expressed concern that terrorists could travel to America disguised as refugees.

For three years, Cruz’s legislation would halt immigration from any nation the State Department has determined contains “territory substantially controlled by a terrorist organization.” After three years, lawmakers would consider whether to extend the prohibition.

The bill specifically mandates a ban on refugees fleeing Iraq, Libya, Somalia, Syria and Yemen.

It  would make a limited exception. Refugees from high-risk countries could circumvent the ban by verifying their refugee status–and only if they belonged to a group “designated as victims of genocide.”

The bill contains no religious test, but the exception appeared to be tailored to Christian victims of genocide.

In the past week, Cruz called on Obama to hold up Syrian Muslims from entering the country but allow Syrian Christians to enter. The senator said he is concerned that Muslim refugees may be affiliates of the Islamic State, also known as ISIS.

“At the end of the day, it’s not that complicated,” Cruz told ABC News on Tuesday. “There’s no history of ISIS terrorists embedding in the Christian community and pretending to be Christian.”

In recent days, Obama has criticized Republicans for rhetoric that he says paints the United States as the enemy of Islam and furthers terrorists’ strategy.

“I cannot think of a more potent recruitment tool for ISIL than some of the rhetoric coming out of here in the course of this debate,” the president told reporters, using another name for ISIS.

But bipartisan support for a general “pause” on Syrian refugees resettling in the U.S. continues to grow in both the House and Senate–and in both parties.

A pause “may be necessary,” the Senate’s third-ranking Democrat, Chuck Schumer, D-N.Y., told reporters Tuesday. “We’re going to look at it.”

During his weekly press conference Tuesday, House Speaker Paul Ryan, R-Wis., warned that a pause in admitting Syrian refugees could be necessary.

“Our nation has always been welcoming, but we cannot let terrorists take advantage of our compassion,” Ryan said. “This is a moment where it’s better to be safe than to be sorry.”

The White House has threatened to veto any bill that mandates more rigorous security checks for Syrian refugees prior to resettlement in the U.S.