The speaker of the City Council, Christine Quinn, and the Reverend Al Sharpton, traded compliments yesterday as they shared a stage to speak out against hate crimes in the city.

Ms. Quinn, considered a likely candidate for mayor in 2009, praised Rev. Sharpton for his public support for gay rights, noting that others have been hesitant to speak out on the issue.

Rev. Sharpton, in turn, thanked Ms. Quinn for bringing residents and city leaders together to act against a recent rise in hate crimes. Ms. Quinn worked with Rev. Sharpton to organize the Day Out Against Hate, which was held yesterday in all five boroughs.

“I would give a lot of credit to the speaker and the council for calling us together,” he said.

Ms. Quinn and Rev. Sharpton, along with Rabbi Michael Miller, spoke to a crowd of clergy representing several religions at the first event of the day, held at Medgar Evers College in Brooklyn. They called on the audience to encourage interfaith communication and to denounce acts of hate. In introducing Rev. Sharpton, Ms. Quinn said one of the ways she judges people is to remember how they treated her before she became speaker.

“I called on Michael Miller and Al Sharpton when I was a staff member to a City Council member, when I was an organizer, when I was a council member, and when I was speaker of the City Council. And every single time they have always, regardless of the title I had, said yes,” she said.

While the reverend and the speaker spoke warmly of each other yesterday, in July, Rev. Sharpton endorsed one of Ms. Quinn’s staunchest critics on the council, Charles Barron, who is running for president of Brooklyn.

Mr. Barron said yesterday that he did not think Rev. Sharpton should be speaking kindly of Ms. Quinn because “she is not a kind person, she’s a dictator.”

“I don’t think he should let her off the hook with some little ‘Day of Hate,'” he said.

Rev. Sharpton’s relationships with past mayors have run the gamut from cordial with Mayor Bloomberg to outright hostile with Mayor Giuliani.