Republicans in the House are pushing for passage of a bill that would put new restrictions on U.S. travel to Syria, which they hope will make it harder for the Islamic State to recruit U.S. fighters.

The bill from Rep. Frank Wolf (R-Va.) was introduced back in March, but it could start to enjoy widespread support in light of the news that two Americans may have died fighting for the Islamic State in Syria this week.

A member of United Nations Disengagement Observer Force Zone (UNDOF) uses binoculars to watch smoke rising in the distance caused by fighting between forces loyal to Syrian President Bashar Assad and rebels over the control of the Quneitra border crossing. Syrian rebels, including Al-Qaeda’s affiliate Al-Nusra Front, seized control of the Syrian crossing with the Israeli-occupied Golan Heights, the Britain-based Syrian Observatory for Human Rights said. AFP PHOTO / JACK GUEZ

In a Thursday letter to his House colleagues, Wolf said that news shows that Congress needs to take steps to prevent Americans who may be sympathetic to the terrorist group from ever reaching Syria. Today, there are no restrictions on U.S. travel to Syria.

“It is imperative that the U.S. take proactive steps to discourage Americans from traveling to Syria to link up with these groups,” Wolf wrote. “Currently, unless the U.S. has solid evidence that they have joined one of these terrorist groups, the FBI can’t detain and arrest suspects upon their return.”

Wolf said one Islamic State agent drove a truck filled with explosives into a building, and then was able to return to his home in Florida. “Incredibly, he traveled to and from Syria with impunity, because there are no restrictions on Americans going there,” he wrote.

Wolf’s bill is the International Conflicts of Concern Act. Introduced in March, it would require the president to identify countries whose governments allow terrorist organizations to operate, and restrict travel by U.S. nationals to those countries.

It also immediately requires Syria to be listed as one of those countries.

“This authority to temporarily restrict unlicensed travel to countries like Syria would provide a powerful new tool to prevent radicalization and keep our nation safe,” Wolf wrote. “It would also still allow for legitimate travel by licensed humanitarian aid workers, journalists and other groups cleared by the U.S. government.”

So far there are just three cosponsors of the bill, all of whom signed onto it on August 1: Reps. Peter King (R-N.Y.), Robert Pittenger (R-N.C.), and Steve Stockman (R-Texas).