In a interview with CBS News White House correspondent Mark Knoller, the vice president also said Gonzales has been truthful in his testimony before Congress.
Senate Judiciary Committee Chairman Pat Leahy, a Democrat, has said he doesn't trust Gonzales, but Cheney said the attorney general has the support of the only man who really counts.
"I've had my differences with Pat Leahy," Cheney said. "I think the key is whether or not he (Gonzales) has the confidence of the president — and he clearly does."
Cheney also discussed the case of his former top aide, I. Lewis "Scooter" Libby. President Bush commuted the 2½-year prison term Libby received following his conviction in the CIA leak case.
The vice president said he disagreed with the jury's guilty verdict.
"You asked me if I disagreed with the verdict, and I did," he said.
That stance differs from that of the president. Mr. Bush said he respected the verdict, but thought the jail term was excessive.
When asked if he would have granted a full pardon to Libby if the choice was his, Cheney said: "I thought the president handled it right. I supported his decision."
Gonzales has received little in the way of public support from Republicans in the face of a concerted attack by the Democrats.
Last week, four Democrats on the Senate Judiciary Committee asked Solicitor General Paul Clement for the special probe of Gonzales. The request came after FBI Director Robert S. Mueller appeared to contradict Gonzales' statements about internal administration dissent over the president's secretive wiretapping program.
Gonzales told that committee the program was not at issue when then-White House counsel Gonzales made a dramatic visit to Attorney General John Ashcroft's hospital room in 2004. Mueller, before the House Judiciary Committee, said it was.
The apparent contradiction only compounded problems for Gonzales, who is losing support among members of both parties even as he retains Mr. Bush's, over a series of apparent misstatements since Congress began investigating the firings of federal prosecutors seven months ago.
Leahy sent a letter to Gonzales last Thursday giving him a week to resolve any inconsistencies in his testimony. While he has declined so far to support a perjury probe, Leahy indicated that could change.
"He has a week," Leahy said Sunday. "If he doesn't correct it, then I think that there are so many errors in there that the pressure will lead very, very heavily to whether it's a special prosecutor, a special counsel, efforts within the Congress."