The White House has finished gathering documents to turn over to the Justice Department in the investigation of a leak that revealed a CIA employee's name and lawyers are reviewing whether the information is relevant to the request.

"The response is substantially complete," a White House official said Tuesday after White House staff met the 5 p.m. deadline set by White House Counsel Alberto Gonzales.

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.

The unnamed official said some staff have not yet turned over whatever documents they may have relating to former Ambassador Joseph Wilson (search) and his wife, whom reporters publicly linked to the CIA in articles this summer. But those staff have extenuating circumstances, such as being overseas, the official said.

Earlier in the day, White House Press Secretary Scott McClellan said it could take as long as two weeks to check submissions from among 2,000 employees for relevance to the criminal inquiry. 

"You don't want to overburden the Department of Justice with documents that have no relevance or are not responsive to their request," he said. "They're welcome to look at the other documents — that's not an issue — that are not responsive to their request."

McClellan would not rule out the possibility that the White House would invoke executive privilege to shield sensitive documents, but said such discussion was premature.

At least one Democratic lawmaker expressed misgivings about the process.

"I am very troubled by the fact that the White House counsel seems to be a gatekeeper, and I want to know what precautions Justice is taking to ensure that it gets all relevant information from the administration," said Sen. Charles Schumer, D-N.Y.

While White House staff scrambled to meet the deadline, President Bush vowed that he will do what he can to find out what led to the woman's name being revealed.

"I want to know the truth. That's why I've instructed this staff of mine to cooperate fully with the investigators; full disclosure and everything we know that the investigators will find out," Bush said during a Cabinet meeting.

But, he added, he has no idea what the investigation will produce or whether the leaker's identity will ever be discovered.

"I have no idea whether we'll find out who the leaker is, partially because, in all due respect to your profession, you do a very good job of protecting the leakers," he said. "You tell me: How many sources have you had that's leaked information that you've exposed or had been exposed? Probably none. I mean, this town is a town full of people who like to leak information."

Leak investigations often founder without clear evidence of who said what to whom, something difficult to establish even from records such as e-mail and phone logs.

Regardless of how the investigation turns out, the administration is eager to be done with it. White House Chief of Staff Andy Card (search) sent a memo to staff earlier Tuesday that read: "The sooner we complete the search and delivery of documents, the sooner the Justice Department can complete its inquiry and the sooner we can all return our full attention to doing the work of the people."

Three journalists — Robert Novak (search) and two Newsday reporters — had identified the CIA employee's name in articles published over the summer. The employee, Valerie Plame (search), a CIA operations officer who has served overseas, is married to Wilson, who publicly accused the Bush administration of manipulating intelligence to exaggerate the threat from Iraq.

Novak said that his source was not in the White House. The Department of Justice has also asked officials at the Defense and State departments and the CIA to preserve any relevant documents.

The Pentagon also set a 5 p.m. Tuesday deadline for collecting relevant documents, but State Department spokesman Richard Boucher said his department had simply been asked to "preserve and maintain" such documents.

McClellan firmly ruled out any role by three administration officials in the leak: political adviser Karl Rove (search), Vice President Dick Cheney's chief of staff, I. Lewis "Scooter" Libby, and National Security Council official Elliott Abrams.

But Rep. John Conyers, D-Mich., the top Democrat on the House Judiciary Committee, said even if Rove was not responsible for the leak, he should resign for talking about it after it happened.

"In my view, it is shameful and unethical that an administration that promised to govern with 'honor and integrity' and 'change the tone' in Washington has now engaged in an orchestrated campaign to smear and intimidate truth-telling critics, placing them in possible physical harm and impairing the efforts and operations of the CIA," Conyers said.

McClellan said that charges about specific officials such as Rove are coming from people who see a political opportunity to attack the White House, and who are less interested in the specific leak and more interested in damaging the administration by floating one name after another as the guilty party.

White House officials say talk of Rove's resigning is just a method of "moving the goal posts."

McClellan took exception to suggestions that the leak was intended to punish Wilson for speaking out.

"If someone in this administration leaked classified information, they will no longer be a part of this administration, because that's not the way this White House operates," he said.

Fox News' Jim Angle and The Associated Press contributed to this report.