Democrats blasted the administration for not acting sooner, while Republicans contended the Democrats' plans would make it too difficult to prosecute terrorists.
The policy, outlined in a new Defense Department memo and congressional testimony, reflects the recent 5-3 Supreme Court decision blocking military tribunals set up by President Bush. The court ruled that the secret tribunals, established by Bush to try suspected terrorists, do not obey international law and had not been authorized by Congress.
CBS News legal analyst Andrew Cohen said the announcement is an about-face ordered in response to the recent Supreme Court decision. He called it "a reversal of policy."
The ruling opened the door for Congress to pass legislation on where and how military detainees could be prosecuted. The Senate is expected to take up legislation addressing the legal rights of suspected terrorists after the August recess.
Click here to read the Department of Defense memo.
But a Pentagon lawyer told the Senate Judiciary Committee on Tuesday that whatever new procedures are adopted for prosecuting members of al Qaeda, there's no way al Qaeda members are going to have the same legal rights as common criminals, CBS News correspondent David Martin reports.
"It is simply not feasible, in time of war, to gather evidence in a manner that meets strict criminal procedural requirements," Deputy General Counsel Daniel J. Dell'Orto said.
The Supreme Court decision rankled many conservatives who have long maintained that the president does not need permission from Congress to detain indefinitely enemy combatants captured on the battlefield.
Although the Bush administration lost the battle over whether the Geneva Convention should apply to members of al Qaeda, the fight over exactly what legal rights they're entitled to is just beginning, Martin reports. Finding a legislative solution to the Supreme Court ruling is "not going to be easy because some of the suggestions on the other side would make it almost impossible to not disclose classified information and in some ways make hearsay evidence unavailable," said Sen. Orrin Hatch, R-Utah, a member of the Judiciary Committee.
Hatch and other conservatives, along with the Bush administration, have said they would oppose prosecuting terror suspects using the military's court-martial system because it could expose sensitive information and hinder interrogations. The system also would prohibit hearsay evidence, which they contend is necessary for convictions of terrorists and common in international military tribunals.
The principal deputy general counsel of the Department of Defense told senators that detainees in Guantanamo are already being treated in accordance with Article 3 of the Geneva Conventions, which specifies how prisoners must be treated, CBS News correspondent Bob Fuss reports.
Democrats say they have largely been shut out of meetings with administration officials on the issue and are frustrated with the White House decision not to prosecute detainees using the existing court-martial system.
Sen. Patrick J. Leahy of Vermont, the top Democrat on the Senate Judiciary Committee, said the court decision "has given our system of constitutional checks and balances a tonic that was sorely needed."
"We need to know why we are being asked to deviate from rules for courts-martial," Leahy said.
"Let's see what the administration comes up with. That's a start," Kyl said, adding that he hopes the Senate will have a sound bill in September.
Steven Bradbury, acting assistant attorney general of the Justice Department's Office of Legal Counsel, told the Senate hearing that the Bush administration would abide by the Supreme Court's ruling that a provision of the Geneva Conventions applies.
But he acknowledged that the provision, which requires humane treatment of captured combatants and requires trials with judicial guarantees "recognized as indispensable by civilized people," is ambiguous and would be hard to interpret.
"The application of common Article 3 will create a degree of uncertainty for those who fight to defend us from terrorist attack," Bradbury said.
The Pentagon stands to gain a lot from this change of policy, Cohen said.
"Now, arguably, our own soldiers around the world have a better chance to gain the protections of the Geneva Conventions from enemy states. I think the reciprocity issue here was a big factor," he said.
White House Press Secretary Tony Snow said efforts to spell out more clearly the rights of detainees does not change the president's determination to work with Congress to enable the administration to proceed with the military tribunals, or commissions. The goal is "to find a way to properly do this in a way consistent with national security," Snow said.
Snow said that the instruction manuals used by the Department of Defense already comply with the humane-treatment provisions of Article 3 of the Geneva Conventions. They are currently being updated to reflect legislation passed by Congress and sponsored by Sen. John McCain, R-Ariz., to more expressly rule out torture.
Speaking after the Supreme Court issued its ruling, President Bush said he would work with Congress to get approval to try terrorism suspects before military tribunals.
On June 29, Mr. Bush said the ruling "won't cause killers to be put out on the street," and added that he "will not jeopardize the safety of the American people."
"The administration intends to work with Congress," Snow said.
"We want to fulfill the mandates of justice, making sure we find a way properly to try people who have been plucked off the battlefields who are not combatants in the traditional sense," he said.
"The Supreme Court pretty much said it's over to you guys (the administration and Congress) to figure out how to do this. And that is where this is headed."