Bush also openly backed Alberto Gonzales, the attorney-general and long-time aide, whose resignation is being demanded by Democrats and some Republicans.
"Congress and the American people deserve a straight answer"
Harry Reid, senate majority leader
The judiciary sub-committee is expected to vote on whether to issue subpoenas for Rove and four other past and present top White House officials, including Harriet Miers, the former counsel.
Miers was initially thought to have raised the idea of firing the 93 prosecutors after Bush's re-election in 2004.
Besides Miers, other White House officials offered for questioning are William Kelley, the deputy counsel, and Scott Jennings, the political adviser.
Bush, who was pressed to remove Donald Rumsfeld, the defence secretary, after the Democrats took the majority in congress, said he would stand by White House officials.
No oath, no transcript
Fred Fielding, Bush's official government lawyer, told legislators that Bush's aides would accept private interviews instead of testifying under oath.
"Such interviews would be private and conducted without the need for an oath, transcript, subsequent testimony, or the subsequent issuance of subpoenas," Fielding said in a letter released by the White House.
Several legislators have criticised Bush for taking a combative stance.
Senator Patrick Leahy, chairman of the Senate Judiciary Committee, rejected Bush's offer for Rove to be questioned privately by prosecutors.
"I don't accept his offer. It is not constructive and it is not helpful to be telling the senate how to do our investigation, or to prejudge its outcome," he said.
Harry Reid, the senate majority leader, said the Bush administration had offered "a bunch of different stories" about why the prosecutors were fired last year.
"Congress and the American people deserve a straight answer," Reid said.
"If Karl Rove plans to tell the truth, he has nothing to fear from being under oath like any other witness."
Gonzales has also come under fire over an internal probe which found that the FBI, part of his department, had breached privacy laws in overzealously seeking access to information about suspected terrorists.
Glenn Fine, the head of the justice department's probe, said he believed the FBI's violations were "serious and unacceptable".
"Our review found widespread and serious misuse of the FBI's national security letter authorities," Fine told the House of Representatives on Tuesday.