Some may view Mayor Bloomberg and the speaker of the City Council as odd political partners, but the two have acted like old friends since Christine Quinn was elected to the post seven weeks ago.

The mayor, a billionaire who made his fortune building a news business, and Ms. Quinn, a former housing advocate who ran a gay and lesbian antiviolence group, appeared together twice last week alone.

On Monday, they stood together to call on Albany to deliver more education money to the city. A few days later, they announced joint legislation to rein in lobbyists and crack down on pay-to-play politics in city government.

The relationship is a glaring contrast to that between Mr. Bloomberg and the last council speaker, Gifford Miller, who was campaigning to take over at City Hall and rarely let a day pass without publicly berating the mayor.

When asked recently whether she was making an effort to steer clear of clashes with the mayor, Ms. Quinn said the two were simply trying to advance city causes.

“If you have two people pulling on the oars at the same time in the same direction, they are going to move the boat much faster up the Hudson River,” Ms. Quinn said during a phone interview. “Are we going to agree all the time? No, but hopefully, we’ll be standing together more times than not.”

Ms. Quinn, who is gay, has toned down her criticisms of the mayor since her election as speaker in early January. Last year, she was one of the loudest critics of the mayor’s proposal to build a football stadium for the Jets on the West Side of Manhattan.

In 2004, she brought a plate of waffles to a press conference to symbolize what she viewed as Mr. Bloomberg’s “waffling” position on gay marriage, and more recently, she has attacked Mr. Bloomberg over a lawsuit he filed to block the equal benefits law.

The law, which was deemed invalid last week by the state’s highest court before it could go into effect, would have barred the city from doing business with companies that don’t provide the same benefits for employees’ gay domestic partners as for employees’ spouses.

When a lower court ruled on the case last year, Ms. Quinn was quoted by the Associated Press as saying: “I’m very disappointed that Mayor Bloomberg is continuing this wrongheaded appeal of the equal benefits bill.”

Last week, however, Ms. Quinn talked about her disappointment with the ruling rather than any ire toward the mayor.

Political analysts said Ms. Quinn’s more recent approach is wise and that this period of amity with the mayor is more than just a political honeymoon. They said it could lay the foundation for a council that acts more like a partner than an enemy to the administration – a shift that could help Ms. Quinn further the council’s policy goals.

Under Mr. Miller, the council overrode more mayoral vetoes than any council before it, but the mayor was able to secure solid public backing.

“She knows that in Gifford’s final year in office the mayor was able to undercut him,” the executive director of the Citizens Union, Dick Dadey, said. “She saw the mistakes Gifford made. She’s not going to make those mistakes.”

A professor of public affairs at Baruch College, Douglas Muzzio, said Ms. Quinn seems to be “moving toward a more conversational, less confrontational” approach.

“She’s got core beliefs, and she obviously feels that working with the mayor is a better way to achieve things than working against him,” Mr. Muzzio said.

A spokesman for Mr. Bloomberg, Stuart Loeser, pointed to Peter Vallone Sr., who served as speaker before Mr. Miller, as an example of a council leader who successfully acted like a partner to the mayors he served with.

“Given the choice between a constructive partner in governing and the alternatives, the mayor certainly prefers a constructive partner,” Mr. Loeser added.

Both Mr. Bloomberg and Ms. Quinn have said they anticipate that there will be disagreements between them. Last week, when asked about their relationship at a press conference at City Hall, Mr. Bloomberg said the two “aren’t always on the same page,” but are “partners in government.”

“There’ll be the normal discourse and … battles,” Mr. Bloomberg said. That’s what democracy is all about. That’s what’s healthy. It’s when you’re not talking that it’s not healthy.”

An unpaid adviser to Mr. Bloomberg, Mitchell Moss, a professor at New York University, said: “It’s always better to start out harmoniously. Your alliances will help you get through the rougher times.”