The committee is examining the accuracy of intelligence about deposed Iraqi President Saddam Hussein's weapons programs and purported contacts with terrorist groups. That intelligence served as Bush's main arguments for the U.S.-led war.
A White House spokesman remained noncommittal, promising "a spirit of cooperation" but no specifics. Spokesman Trent Duffy reiterated administration doubts about the committee's jurisdiction over the White House.
The CIA and the State Department already turned over large quantities of documents ahead of the committee's deadline last Friday and more material is coming, said Republican Sen. Pat Roberts.
White House acquiescence, on behalf of the National Security Council, came to committee staff members late Friday along with notification from the Pentagon that it also would cooperate, Roberts said on CNN's "Late Edition."
The committee's top Democrat, Sen. Jay Rockefeller, said he wants "to see the documentation before ... I'm satisfied. I want to know that we really have it in hand."
Roberts, who was in Kansas, spoke just after Rockefeller, in Washington, had complained that the White House and Defense Department were "being very resistant."
Rockefeller had just finished saying, "We have to have those documents. We're going to get those documents, one way or another," when Roberts was asked if he concurred.
"Well, that's yesterday's story," the chairman said.
Roberts said he had not had the chance to call Rockefeller over the weekend to report the latest development: the White House's agreement "in a spirit of cooperation" to the committee's demands.
Duffy, with President George W. Bush in Crawford, Texas, repeated that phrase in a conference call with reporters but offered no concrete promises. He would not confirm Roberts' assertion that the White House has agreed to turn over the documents the committee seeks.
"We've had productive conversations about ways we can work with and assist the committee," Duffy said. "While the committee's jurisdiction does not cover the White House, we want to be helpful and we will continue to talk to and work with the committee in a spirit of cooperation."
After the deadline passed Friday, both senators accused the White House of ignoring the committee's demand for documents and access to officials for interviews it needed in its work.
"It is certainly good news that there is a spirit of cooperation with the White House," Roberts said. "The challenging news is, however, that we have to fold this new information into all of the work that we have done."
He said the committee would like to expedite its final report, "but the most important thing to do is to get an accurate and complete picture." A top White House official had promised every document requested would be surrendered, he said.
On Friday, White House spokesman Scott McClellan promised to cooperate with the committee even though he said it lacked jurisdiction to ask for it.
Rockefeller took issue with that, saying the committee's job involves not only "rigorous oversight of the collection and analysis of intelligence, but also the use of intelligence, and that includes all of the U.S. government. That includes policy-making, defense and national security."
The Bush administration also is in a battle of wills with an independent commission studying circumstances of the Sept. 11, 2001, attacks. The commission, which has a May 27, 2004, deadline to complete its report, has threatened to issue subpoenas unless the requested documents are provided quickly.