"I'm pleased we have agreement," said Senate Majority Leader Bill Frist, emerging from a session in his office where national security adviser Stephen Hadley and key lawmakers reviewed the compromise.
Hadley called it a "framework for compromise," and Sen. John Warner said he will not consider the agreement sealed until President Bush signs it.
President Bush hailed the agreement, saying it will "help us crack the terror network to save American lives."
Mr. Bush thanked the Senate for the deal and said it will allow the CIA to continue interrogations of suspected terrorists. Mr. Bush said he hopes the legislation passes before Congress adjourns next week, reports CBS News correspondent Mark Knoller.
An accord would fulfill a Republican political and legislative imperative — pre-election party unity on an issue related to terrorism, and possible enactment of one of Mr. Bush's top remaining priorities of the year.
"The agreement that we've entered into gives the president the tools he needs to continue to fight the war on terror and bring these evil people to justice," said Sen. John McCain, one of three rebellious lawmakers who told Mr. Bush he could not have the legislation the way he initially asked for it.
"There's no doubt that the integrity and letter and spirit of the Geneva Conventions have been preserved," he said.
The Geneva Conventions prescribe international standards for the treatment of prisoners taken in a war.
Details of the agreement - which hours later, sparked- were sketchy.
The central sticking point had involved a demand from McCain, Warner and Sen. Lindsey Graham for a provision making it clear that torture of suspects would be barred. The three gathered in the afternoon to work out language for the deal, reports CBS News correspondent Sharyl Attkisson.
One official said that under the agreement, the administration agreed to drop language that would have stated an existing ban on cruel, inhuman or degrading treatment was enough to meet Geneva Convention obligations. Geneva Convention standards are much broader and include a prohibition on "outrages" against "personal dignity."
In turn, this official said, negotiators agreed to clarify what acts constitute a war crime. The official spoke on condition of anonymity, saying he had not been authorized to discuss the details.