Republican lawmakers are reviving a push to strip American citizenship for those who link up with foreign terrorist groups, in response to Islamic State recruitment efforts. 

Sen. Ted Cruz, R-Texas, filed a bill on Monday that would impose that punishment for Americans who join the Islamic State, also known as ISIS, or any other foreign terror organization. 

"There are over 100 Americans right now who have gone and are fighting alongside ISIS," Cruz told Fox News on Monday. He said "we can't have people who have joined the terrorists, using U.S. passports to come back and commit acts of terror here at home." 

Efforts to strip U.S. citizenship for those who try to join terror groups have surfaced before, but run into complicated legal questions. Currently, U.S. citizenship can only be taken away voluntarily. 

But the measure, filed as lawmakers returned to Capitol Hill following a month-long summer break, is one of several pending pieces of legislation dealing with the ISIS threat. While some focus on the citizenship aspect, others are pushing for a vote on the Hill to authorize further military action. 

Cruz said he hopes to get bipartisan support for his proposal. His bill amends existing law that lays out conditions under which an American could renounce their citizenship to include becoming a member of a terrorist group, fighting for a foreign terrorist organization that is working to carry out attacks against the U.S. or its citizens or providing material assistance to a terror group.

"There can be no clearer renunciation of their citizenship in the United States, and we need to do everything we can to preempt any attempt on their part to re-enter our country and carry out further attacks on American civilians," he said in a statement. 

Rep. Michele Bachmann, R-Minn., a member of the House Intelligence Committee, introduced similar legislation on Monday as well.

“By turning against their country, their passports should be revoked and if they’re naturalized citizens, they should lose their citizenship,” Bachmann said in a statement. “As elected officials, protecting our nation and keeping the American people safe is our highest duty. In light of the growing threat of terrorist groups like ISIS and al-Shabaab, I urge House and Senate leaders to fast track this legislation and for the President to sign it.”

A bipartisan group of senators from the home states of murdered journalists James Foley and Steve Sotloff also introduced bills that would authorize $10 million in reward money to catch their killers. 

The legislation from Sens. Marco Rubio, R-Fla.; Bill Nelson, D-Fla.; Jeanne Shaheen, D-N.H.; Kelly Ayotte, R-N.H.; and Cruz would update the State Department’s Rewards for Justice Program to include the murders of the journalists. The program has paid out more than $125 million in return for actionable intelligence since 1984.

Sotloff was from Florida, and Foley was from New Hampshire.