Updated

President Bush was questioned for more than an hour by government prosecutors Thursday as part of the probe into who leaked the name a CIA operative to the media.

The president was questioned for 70 minutes in the Oval Office by U.S. Attorney Patrick J. Fitzgerald (search), who is heading the Justice Department investigation.

White House press secretary Scott McClellan (search) said Bush has hired a private attorney, Jim Sharp, a Washington trial lawyer and former federal prosecutor.

"The leaking of classified information is a very serious matter," McClellan said, adding that the president repeatedly has said that he wants his administration to cooperate with the investigation.

"No one wants to get to the bottom of this matter more than the President of the United States, and he has said on more than one occasion that if anyone — inside or outside the government — has information that can help the investigators get to the bottom of this, they should provide that information to the officials in charge," McClellan said.

Fitzgerald spokesman Randall Samborn declined comment on the probe and on the Bush interview.

Investigators want to know who leaked the name of Valerie Plame (search), an undercover CIA operative, to syndicated columnist Robert Novak last July. A federal grand jury in recent months has questioned numerous White House and administration officials.

All indications are that investigators are winding down their probe, with one of the last steps being interviewing Bush

Fox News has learned that an outside supporter of the president who has already testified before the grand jury was also visited Thursday by the FBI, which spent the afternoon downloading all his computer files.

The grand jury meets Friday to hear more evidence in the case.

Disclosure of an undercover officer's identity can be a federal crime.

McClellan said Bush was "pleased to share whatever information he had with the officials in charge, and answer their questions."

McClellan told reporters Thursday that any further questions regarding the investigation should be directed toward the officials at the U.S. Attorneys office, who are in charge of the probe.

Vice President Dick Cheney was also recently questioned by investigators, it was learned earlier this month.

Fitzgerald, of Chicago, was chosen to run the investigation in late December after Attorney General John Ashcroft disqualified himself from the politically sensitive case to avoid an appearance of conflict of interest.

Wilson has said he believes his wife's identity was disclosed to attack his credibility because he criticized Bush administration claims that Iraq under Saddam Hussein had tried to obtain uranium from Niger. Wilson went to Niger for the CIA to investigate the information about Iraq and he found the allegation to be highly unlikely.

Syndicated columnist Robert Novak revealed Plame's work for the CIA a week after Wilson publicly criticized Bush's claim that Iraq had tried to obtain the uranium.

Fox News' Anna Stolley and The Associated Press contributed to this report.