Just before a campaign speech in Illinois, Mr Bush said to his running mate Dick Cheney: "There's Adam Clymer, major league asshole from the New York Times."
Mr Bush later said he did not realise that live microphones were going to pick up the remark, but he stopped short of an actual apology.
A BBC correspondent says that the Texas governor appeared shaken by the gaffe, which came as he started the final phase of campaigning for November's election.
Not the first time
Asked if "calling people names" was part of the campaign, Mr Cheney said: "The governor made a private comment to me."
Mr Bush has been unhappy with several articles by Mr Clymer which were critical of his record.
The BBC Washington correspondent, Philippa Thomas, says that the incident is every politician's nightmare and it has happened to the Texas governor before.
On the campaign trail on Tuesday, Mr Bush returned to his normal agenda, delivering a speech about making medical benefits more widely available.
Democrats' delight
But the Gore campaign was quick to seize on Mr Bush's mistake, with a spokesman declaring that the Democrats had high regard for journalists.
"We hold virtually all members of the Fourth Estate in the highest regard and we believe they should be part of the democratic process day in and day out," Democratic spokesman Chris Lehane said.
"It's the second time in less than a week that the governor has broken his promise to 'change the tone' of the campaign.
"First, he used an ad to attack the vice-president in a very nasty and personal way, now he's used an expletive to attack a member of the working press," added Mr Lehane.
Key states
With nine weeks to go, both presidential candidates are engaged in a sweep across key battleground states.
Vice-president Gore himself has been speaking about his plans to sustain the nation's economic growth, after a weekend of non-stop campaigning.
In the last two weeks Mr Gore has been buoyed by opinion polls which show him pulling ahead of his rival.
A Newsweek poll on Friday showed Mr Gore on 49% to Mr Bush's 39% - with Green Party nominee Ralph Nader receiving 3% and the Reform Party's Pat Buchanan 1%.