Accepting the Independence Party’s endorsement seems to be getting trickier for candidates, including Mayor Bloomberg, who has the party to thank for delivering his margin of victory in the last election.

Yesterday, two party members, Frank Morano of Staten Island and Michael Zumbluskas of Manhattan, standing on the steps of City Hall, urged candidates to renounce their ballot line until one of the party’s leaders, Lenora Fulani, steps down.

Ms. Fulani has been accused of making anti-Semitic remarks, from which in a recent television interview on NY1 News she declined to back away. The interview aggravated an existing conundrum for Mr. Bloomberg, who won 59,000 votes on the Independence Party line in 2001, shepherding him into office with just 35,500 votes more than his Democratic opponent, Mark Green. Mr. Bloomberg has called Ms. Fulani’s statements “phenomenally offensive” but said they do not reflect Independence Party members’ views. His campaign staff has also pointed out that many Democratic candidates, including Senator Schumer and Attorney General Eliot Spitzer, have accepted the party’s ballot line in the past.

Mr. Morano, who is on the party’s state committee, and Mr. Zumbluskas, the party’s former Manhattan chairman, however, said Ms. Fulani has to go.

“Her positions do not coincide with what the rank-and-file members of the Independence Party believe,” Mr. Morano said during a phone interview after his new conference.

The men were joined by a member of the City Council, Lewis Fidler, who plans to introduce a resolution today that denounces Ms. Fulani’s comments as “racist, bigoted, anti-Semitic, and inappropriate.”

“To allow statements like that to go unchallenged by someone with a title and influence in a party that gets automatic ballot access in the state of New York is just wrong,” Mr. Fidler said.

The resolution has support from 19 council members and the speaker of the council, Gifford Miller, one of four Democrats hoping to replace the mayor. Mr. Miller accepted the Independence line when he won election to the council but has not sought it since.

An official of the Independence Party, Jacqueline Salit, said yesterday the resolution was “unconstitutional” and “political grandstanding.”

Ms. Salit said she had “every reason to believe” Mr. Bloomberg would run on the party line.

The latest development follows an announcement last week by Council Member Eva Moskowitz that she was rejecting the party in her bid to become the next borough president of Manhattan.

A Bloomberg campaign spokesman, William Cunningham, said Mr. Bloomberg agreed with Mr. Morano that Ms. Fulani’s views were not representative of the party. Mr. Cunningham also said the mayor has “fought prejudice and racism his whole life.”