Asked by debate moderator Peter Jennings to say whether Mr Gore had ever taken a quote or vote out of context, his opponent instantly replied, "Yes".
In a televised debate at the University of New Hampshire, Mr Bradley accused the vice-president of deliberately distorting his proposal to expand health coverage. But Mr Gore responded by saying that his rival's plan was "entirely inadequate" for the poor and others.
Asked by debate moderator Peter Jennings to say whether Mr Gore had ever taken a quote or vote out of context, his opponent instantly replied, "Yes".
The vice president, Mr Bradley said, "offended me" by saying his healthcare plan would shortchange many Americans.
But Mr Gore, paraphrasing Harry Truman, replied: "I'm not giving him hell. I'm just telling the truth and he thinks it's hell."
Both candidates are seeking to gain the upper hand with just weeks to go before the first real test of voter opinion in the Iowa caucus towards the end of January.
Mr Gore is the national frontrunner, but polls in the key primary state of New Hampshire show Mr Bradley leading.
However, the BBC's Nick Bryant in Washington says the race for the New Hampshire primary on 1 February is tantalisingly close.
The New Hampshire primary is being seen as increasingly crucial, and Mr Bradley, a former basketball star, is investing much of his time and money in winning in the state.
Mr Bradley is hoping a win in the state will "wound" the vice-president and give him the momentum to go on to win the Democratic nomination.
Wednesday's debate was the first in a series of showdowns in which Democrats and Republicans will take turns debating in the run-up to the first voting of the presidential campaign.
The Republican Party is holding its first debate later on Thursday between the favourite, George W Bush, and his five current challengers.
Russian policy
Mr Bradley said the US had not pushed hard enough to reduce the stockpile of nuclear weapons and had agreed to send international aid to Russia "knowing that corruption was rampant".
Mr Gore responded: "I think that in spite of the problems there have been some successes, including a new leader committed to reform, a free press and free elections."
"Your underdog pitch brings tears to my eyes," Mr Bradley said.
Mr Gore replied: "I hope that my upset victory brings tears to your eyes on 1 February (in New Hampshire)."
Kennedy support
Earlier, Mr Gore received a welcome boost to his campaign when Senator Ted Kennedy gave him his formal endorsement.
"You have the ability, the vision and the experience and the wisdom to lead our country in the year 2000 and in the years ahead," Mr Kennedy said in an appearance with Mr Gore in Massachusetts.
The endorsement of the head of the Kennedy dynasty is seen as a substantial gain for Mr Gore who faces a strong challenge from former Senator Bradley.
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