Democratic presidential candidate Bill Bradley, offended by criticism from Vice President Gore that his health care plan costs twice as much as Bradley has estimated, fired back yesterday by accusing Gore of promising to expand various domestic programs without telling the public how he would pay for them.

The conflict between the two campaigns signaled a new phase in the fight for the Democratic nomination, with Gore and Bradley beginning to engage one another directly for the first time. The growing debate, while mired in numbers and budgetary estimates, goes to the heart of how both campaigns hope to weaken the other.

Gore has been trying for weeks to engage Bradley on everything from the number of debates the two should have to the former New Jersey senator's voting record to the details of Bradley's domestic proposals. Until now, Bradley largely ignored those attacks, but in the aftermath of Wednesday's town hall meeting in New Hampshire, there has been an escalation in hostility between the two campaigns.

Gore is attempting to undermine Bradley's effort to portray himself as a truth-teller who is not a typical politician. By puncturing the cost estimates of the centerpiece of Bradley's domestic agenda, a plan to dramatically expand health care coverage to 45 million Americans without insurance, Gore hopes to raise broader questions about Bradley's credibility and political character.

Bradley, in turn, hopes to paint Gore as a typical politician who will promise anything to get elected and who lacks the discipline to establish clear priorities and the commitment to tackle big problems with bold ideas.

The Bradley campaign issued a critique of Gore's performance on Wednesday night that was entitled "promises without price tags." The memorandum enumerated a series of statements Gore made in the forum, from public financing of political campaigns and expanded education programs to environmental or energy tax incentives.

"When you put out an agenda, it's appropriate to say what it will cost," said Eric Hauser, Bradley's press secretary. "We said that at the beginning of this campaign even when we hadn't put out an issue agenda."

Chris Lehane, Gore's press secretary, said Bradley's campaign was off base, arguing that the vice president's campaign had walked several news organizations, including The Washington Post, through the details of his spending programs to show much the programs cost and where the money would come from to pay for them.

"The fundamental fact is we put those numbers out to [The Post] and to the Associated Press," he said. "It would be inaccurate to say we haven't put numbers to those programs." The Gore campaign did so, however, only at the request of The Post; moreover, it adjusted some of Gore's promises so that his spending programs did not exceed the projected surplus.

Lehane charged that Bradley has spent the entire projected surplus on his health care plan and would have nothing left for other domestic initiatives. "It takes discipline to make sure you can balance the budget and invest in people and that's what we're doing," he said.

Hoping to put Bradley's charge to rest, Elaine Kamarck, Gore's senior policy adviser, said yesterday that in the next few days, the campaign would post on its Web site what each of the vice president's proposals would cost.

With the Congressional Budget Office estimating surpluses of $3 trillion over the next 10 years, Kamarck said Gore could meet his promises and keep the budget in balance. She said it would take $1.8 trillion to save Social Security and that Gore would allocate another $374 billion for preserving Medicare and providing prescription drug benefits.

Five other spending categories would consume the rest: $146 billion for Gore's health care plan; $127 billion for the military; $115 billion for education; $190 billion for other initiatives;" and $132 billion for financing costs.

"We'll put up our surplus plan and then they'll have to put up their surplus plan," she said. "Even using their own numbers, they've got some problems."

Hauser also accused the Gore campaign of duplicity in citing a study by Ken Thorpe of Emory University that says Bradley underestimated the cost of his health care plan. Hauser said Emory has described Thorpe as a Gore adviser. Kamarck said that, while Thorpe was a Clinton administration official, he has not been part of the Gore campaign.