Howard stated his case for remaining as prime minister during a meeting at parliament house in Canberra of MPs from his ruling Liberal Party.
"There was absolutely no evidence in that party meeting of any desire on the part of the party for any change in the current leadership team," Howard told the Sydney radio station 2GB.
"My view is ... making a change now would be seen by the public as a sign of panic."
Polls throughout the year have indicated that Howard is leading his 11-year-old coalition government to a landslide defeat.
Howard, who first came to power in 1996, put would-be challengers on notice when he told reporters on Tuesday that "I have never run from a fight before and I don't intend to do so now".