The McCain and Graham provisions are not in the House-passed defense bills.
The Senate's approval of Graham's amendment followed Monday's Supreme Court decision to review a constitutional challenge to the Bush administration's military trials for suspected foreign terrorists held at the U.S. naval base in Cuba.
In 2004, the Supreme Court said the 500 or so prisoners held there could file habeas corpus petitions in U.S. courts to fight their detentions. Many of the prisoners were captured in Afghanistan and have been held at Guantanamo for several years without being charged.
Since that ruling, prisoner lawsuits against the government have piled up.
Graham sought to curb what he called "lawsuit abuse," arguing that prisoners of war and enemy combatants have never before been given access to U.S. courts.
But Sen. Carl Levin, D-Mich., said it was too broad and would effectively reverse the Supreme Court's previous decision on the issue of detainees rights. "It is inconsistent with what the Supreme Court did," he said.
Human-rights groups also cried foul.
"Depriving an entire branch of government of its ability to exercise meaningful oversight is a decidedly wrong course to take," said Elisa Massimino, the Washington director of Human Rights First.
On Iraq, Senate Democrats offered a proposal requiring the president to outline a timetable for a phased withdrawal of U.S. forces, and Republicans put forth their own Iraqi policy proposal. Votes on both are expected next week.
