Mr. Green said that during several conversations in the past year, Mr. Nader told him that he did not have huge problems with Mr. Kerry's record.

But Mr. Green said that Mr. Nader ''believes that he'll bring out new voters who will help Democrats win the Senate and House and that he can make a case against Bush like no one else and pull the Democratic nominee toward a more populist position.''

Mr. Green said that he, in turn, told Mr. Nader that during a talk Mr. Green recently gave about his new critique of Mr. Bush, ''The Book on Bush,'' 93 of 100 audience members who said they voted for Mr. Nader in 2000 said they would not do so again. ''I relayed that as a way to say, a) It may hurt Kerry and help re-elect Bush and b) It won't help you given how much more you have to contribute.''

Representative Bernie Sanders, the liberal independent from Vermont, made a similar argument in a statement released last night, which said Mr. Nader ''should not help re-elect George Bush by splitting the vote with the Democratic candidate.''

Despite their statement, aides to Mr. Kerry sought to downplay fears about Mr. Nader last night, arguing that Mr. Nader would likely not be able to draw as much support in 2004 as he did in 2000 - when he drew 2.8 percent of the popular vote. Because Democrats are so focused on defeating Mr. Bush, they said, liberal voters would be less likely to file protest votes.

Mr. Kerry's rival, Senator John Edwards of North Carolina, used the speculation as an opportunity to get in a dig at his opponent, saying ''If we have candidates at the top of the ticket who would appeal to the kind of independents who would vote for Nader, we'll be fine.''

Mr. Nader declined to put all of this to rest last night. A spokeswoman for Mr. Nader, Linda Schade, said everybody would have to wait until he appears Sunday on NBC's ''Meet the Press'' In the meantime, she added, ''this is pure speculation.''

Correction: February 24, 2004, Tuesday An article on Saturday about Democrats' appeals to Ralph Nader to refrain from seeking the presidency, a run they said could help re-elect President Bush, truncated the title of a book by one such Democrat, Mark Green, and omitted the name of his co-author. The title is ''The Book on Bush: How George W. (Mis)Leads America'' (Viking Penguin, 2004). The co-author was Eric Alterman.