Sen. Ted Cruz, R-Texas, is renewing a push for Congress to pass legislation that would revoke the citizenship of any American who tries to join the Islamic State or other terrorist groups.

Cruz thinks that banning people from terrorist-stricken countries from entering the U.S. only deals with half of the problem, and that the federal government also needs to worry about U.S. citizens who may try the same thing.

"If an American citizen travels abroad and joins a terrorist group waging jihad on America, attempting to murder innocent Americans, this legislation would strip that individual of their U.S. citizenship, so that we would not have terrorists returning to America using U.S. passports," Cruz told the Washington Examiner.

Hundreds of Americans have tried to join the Islamic State in recent years, according to Cruz. He said another 124 U.S. citizens or green card holders have traveled overseas to join other jihadist groups in the years since the September 11, 2001 terrorist attacks. "This should be an idea that even Senate Democrats can support given that Hillary Clinton, when she was in the Senate, supported very similar legislation," he said.

Previous iterations of the bill have drawn opposition from some civil libertarians, who worry it would give the federal government expanded powers to revoke citizenship without due process. Under Cruz's bill, anyone who lost their citizenship over alleged terrorist ties would have 60 days to request a due process hearing to challenge the decision.

"The awesome and horrible power of being able to take away the citizenship of an American citizen would be turned over to an unnamed bureaucrat," Christopher Anders, senior legislative counsel for the American Civil Liberties Union's Washington legislative office, told USA Today last year. "It's a highly unconstitutional bill. If it were to become law, I'm sure the Supreme Court would not let it stand."

Cruz's team maintains that's unfair, because his bill — which is being introduced in the House by Rep. Steve King, R-Iowa — uses the same process to revoke citizenship from terrorists that the government has used since 1926 to revoke citizenship from Americans who join foreign armies at war with the United States.

"This legislation is a common sense step to recognize that people can [wage] war against America in more ways than one," he said. "You don't need to be a member of a nation-state military to be a terrorist at war with America."

Trump's presence in the Oval Office could increase the odds that the legislation passes this Congress. Additionally, a former Cruz staffer, Victoria Coates, now works for the White House National Security Council.

"Our office is conferring on a daily basis with the White House and new administration on this matter and a host of other matters as we work together to deliver on the promises made to the American people," Cruz said.