He was responding to questions at his first press conference for four months, after speculation that the White House was considering replacing Mr Cheney for someone younger and fitter in the 2004 election.
Mr Cheney, who is 61, had four heart attacks before becoming vice-president in January 2001.
Later that year he had a pacemaker implanted to monitor his heart and adjust its rhythm if necessary.
The president said he had not made a decision whether to run again in 2004 but if he did he would do so alongside Mr Cheney, who he said had done "an excellent job".
The president also gave his deputy part of the credit for the Republicans' successes in Tuesday's elections
"He was out there toiling along, working hard and turning out the vote," he said.
The vice-president raised more than $40m for Republican candidates, second only to Mr Bush himself, who raised $140m.
