Bush is hoping to send a message to administration officials that leaks will not be tolerated.
"I'd like to know who leaked," Bush said on Monday after meeting the president of Kenya.
"I have told my staff, I want full cooperation with the Justice Department. And when they ask for information, we expect the information to be delivered on a timely basis. I expect it to be delivered on a timely basis," he added.
About 2000 White House employees are scrambling to meet Wednesday's 00:00 (Tuesday’s 21:00 GMT) deadline to deliver documents pertaining to the department’s investigation.
White House spokesman told reporters at least 500 employees had already turned over relevant documents, or declared they had none.
"This is a very serious matter and our administration takes it seriously," Bush said, adding he expected "a good, thorough investigation, which apparently is going to happen soon."
"There's a lot of leaking in Washington, DC. It's a town famous for it"
Revealing classified information is a federal crime which is punishable by up to 10 years in prison.
The investigation stemmed from the disclosure in a newspaper column in July that the wife of a former US envoy in Iraq and Gabon, Joseph Wilson, was an undercover CIA officer specialising in weapons of mass destruction.
Wilson has said Bush administration officials made his wife’s name public in order to muzzle criticism over the Iraq war.
He also said that it was an act of revenge, after he accused the White House of exaggerating the weapons threat from Iraq – Washington’s main justification for going to war.
Wilson went to Niger in February 2002 at the CIA's request to assess a report that Iraq sought to buy uranium from Niger. Wilson found the allegation to be highly doubtful.
Bush said he could not say whether Wilson’s wife, Valerie Plame's name was leaked as retaliation.
McClellan said 500 employees have
turned over documents
"I don't know who leaked the information, for starters, so it's hard for me to answer that question until I find out the truth," Bush said.
He added that he hoped the investigation would help deter leaks of classified information to the press in future.
"There's a lot of leaking in Washington, DC. It's a town famous for it," Bush said. "But hopefully we'll help send a clear signal we expect other leaks to stop as well."
In a notice to all White House employees, White House Counsel Alberto Gonzales requested all documents about Wilson's trip to Niger and his wife's "relationship" with the CIA, as well as any contact with any member of the news media about Wilson, his trip or where his wife works.
Gonzales said he gave the employees until 7 October "to ensure compliance with the time deadlines imposed" by the Justice Department.