Charles Dharapak, Pool, Associated Press
Republican presidential candidates, from left to right: Texas Gov. Rick Perry; former Pennsylvania Sen. Rick Santorum; former Massachusetts Gov. Mitt Romney; former House Speaker Newt Gingrich; and Rep. Ron Paul, R-Texas, participate in the South Carolina Republican presidential candidate debate in Myrtle Beach, S.C., Monday, Jan. 16, 2012.

MYRTLE BEACH, S.C. — The Republican candidates have sharp disagreements over a new policy to detain American citizens suspected of terrorism.

President Barack Obama signed the National Defense Authorization Act that would allow indefinite detention of such terror suspects. Many civil liberties activists believe the law is unconstitutional.

Front-runner Mitt Romney said he would have signed the law and insisted it was "appropriate" to detain American members of al-Qaida. Romney called membership in the group "treason" and said the U.S. government has the right to impose indefinite detention.

Rick Santorum said a U.S. citizen who is detained as an enemy combatant should have the right to a lawyer and to appeal their case before a federal court.

Ron Paul said holding American citizens indefinitely is a breach of the U.S. judicial system.