It is possible some material could be withheld on grounds of national security or executive privilege, CBS News White House Correspondent Mark Knoller reports.
The documents are only part of the investigation. CBS News has learned that the Justice Department has begun to make arrangements to question White House officials.
President Bush said he wants the Justice Department's investigation completed "as quickly as possible."
"I want to know the truth. I want to see to it that the truth prevails," he told reporters Tuesday after a meeting with his Cabinet.
Investigators are trying to determine who leaked to columnist Robert Novak — he wrote that it was "two senior administration officials" — and two Newsday journalists the identity of an undercover CIA operations officer who has served overseas.
The agent is married to former Ambassador Joseph Wilson, who accused the Bush administration in The New York Times of manipulating intelligence to exaggerate the threat from Iraq to justify the U.S.-led invasion.
Mr. Bush's spokesman, Scott McClellan, said Tuesday that the White House counsel's office would turn over to the Justice Department only materials it deemed "responsive or relevant" to the department's criminal inquiry.
Approximately 2,000 White House employees were told to certify by end of business Tuesday either that they had produced all such documents they had or that they had none to produce.
McClellan said that with many aides probably "going above and beyond to make sure that nothing is left out," the volume of materials could bury Justice investigators unless the counsel's office sifted through them first. The sifting could take as long as two weeks, he said.
"A lot of that information may have no relevance or not be responsive to the request from the Department of Justice, and it could slow down their investigation if they're getting volumes of documents that have no relevance," he said.
McClellan would not rule out that the White House might invoke executive privilege for some of the documents. That's a doctrine recognized by the courts that ensures presidents can get candid advice without fear it will become public. "It's premature to even speculate about such matters," McClellan said.
Despite his avowed determination to find the leaker, Mr. Bush alternately expressed confidence and doubt that the leaker would be found.
"They'll come to the bottom of this," he said, but added later: "I don't know if we're going to find out the senior administration official. Now, this is a large administration and there's a lot of senior officials. … I have no idea whether we'll find out who the leaker is."
Should the effort fail, he said, part of the blame falls on journalists, because they "do a very good job of protecting the leakers."
"You tell me: How many sources have you had that's leaked information that you've exposed or had been exposed? Probably none," he told his questioners.
McClellan said his conversations with top political adviser Karl Rove; Vice President Dick Cheney's chief of staff, I. Lewis "Scooter" Libby; and National Security Council official Elliott Abrams have ruled out their involvement. There has been speculation about all three.
In a memo Tuesday afternoon, Bush chief of staff Andrew Card reminded all staff of the White House's self-imposed 5 p.m. deadline. The Justice Department wants the White House to turn over all materials by the middle of the month, the more relevant ones sooner.
The document dump had lawyers from the counsel's office gathered in a room in the building next to the White House late Tuesday, poring over piles of electronic records, telephone logs, correspondence, computer records, notes and calendar entries walked over by Bush aides.
The Pentagon also set a 5 p.m. Tuesday deadline for collecting relevant documents. At the State Department, spokesman Richard Boucher said aides had simply been asked to "preserve and maintain" such documents.
The CIA also has been asked to preserve relevant documents.
At the CIA's behest, Wilson traveled to Niger in early 2002 to probe claims that Iraq tried to buy uranium there. Wilson found no basis for the charge, but Mr. Bush made the allegation in his State of the Union speech.
After Wilson's column appeared, the White House retracted the Niger allegation — its sole admission to date of a flaw in the case for war, which was built on charges of an illegal Iraqi arsenal that has not been found.