Bush had signaled his reluctance to do so just a day earlier, saying he wanted to get rid of such ads but that Gore couldn't be counted on to abide by such a deal. "I don't trust him, to be frank with you," the Texas governor said.

Still, advocates of such a ban hoped Gore's offer would be a step toward eliminating a source of campaign advertising money that now far outstrips spending by the candidates themselves.

Soft money refers to the unlimited contributions gathered by political parties, which can be used to promote a candidate or knock down the opposition but must stop short of telling people who to vote for.

Gore also said he would urge independent organizations to stop running ads aimed at influencing the presidential race -- again only if Bush would too.

Bush's campaign poured cold water on the proposal, calling it "nothing new."

"This is the same tactic that Al Gore tried in March when he said he would forgo soft money while he was raising millions of dollars in soft money," spokesman Ari Fleischer said Wednesday, referring to a soft-money ban Gore proposed just after clinching the nomination in March.

Gore's latest offer came in a letter to the Senate's leading supporters of campaign finance legislation, Sens. John McCain, R-Ariz., and Russell Feingold, D-Wis.

The senators have urged a soft-money ban both for the presidential race and for House and Senate candidates. But even some Democrats are reluctant to give up such a big source of money.

"As soon as John McCain agrees to stop campaigning for Republican candidates who refuse to support campaign finance reform, we'll consider taking him up on this challenge," said Laura Nichols, an aide to House Democratic Leader Richard Gephardt.

Feingold said Gore's offer was "a huge milestone in our effort to get soft money out of the system." For those skeptical that the presidential candidates would ever forgo such a huge pot of ad money, Feingold noted that many people were surprised when Hillary Rodham Clinton and New York Rep. Rick Lazio agreed last weekend to ban soft-money ads in their Senate campaign.

"This thing tends to have a life of its own, because it's tainted money," Feingold said. "Soft money is a corruption of our system, and no candidate should be comfortable being associated with it."

Larry Makinson, executive director of the Center for Responsive Politics, said he wasn't "getting my hopes up" for an end to soft-money ads. But he said the New York Senate deal showed unpredictable things could happen.

Scott Harshbarger, president of Common Cause, welcomed Gore's offer but said it was a sad situation to be congratulating the vice president for agreeing to eliminate what the watchdog group views as an illegal source of campaign ad money. "

Bush, interviewed Tuesday on CNN's "Larry King Live," said it would be hard to ban soft money ads midway through the campaign, after Republicans had been outspent this summer. "It's kind of like, OK, fine, now we fired our weapons, you lay down your arms," he said.

Party spending on soft-money ads is dominating this year's presidential campaign.

Since June 1, the Republican and Democratic parties have spent in excess of $52 million on ads, while combined spending by the Gore and Bush campaigns was $21 million, according to a study by the Brennan Center for Justice at the New York University School of Law in conjunction with political scientist Kenneth Goldstein of the University of Wisconsin-Madison.

Last March, Gore pledged to hold back Democratic Party ads until the Republicans fired the first shot, but both parties ended up advertising heavily for their candidates.