On a Saturday night in early December, two of the Democratic mayoral candidates, Gifford Miller and Anthony Weiner, found themselves under a massive tent in Williamsburg, wearing black yarmulkes, at a religious celebration with the chasidic Satmar community.

The fresh-faced Mr. Miller, 35, a Protestant who represents Manhattan’s Upper East Side and serves as speaker of the City Council, wore a yarmulke with the word “Gifford” embroidered in gold-colored thread in Hebrew lettering.

Though it is not surprising that either Mr. Miller or Mr. Weiner, a member of Congress who is Jewish, paid the chasidic community a visit – it is essentially a prerequisite for anyone running for citywide office – their appearances signal that the candidates who want to replace Mayor Bloomberg have begun the delicate process of courting support among a group that will undoubtedly have influence in the upcoming election.

“The chasidic community has always been a swing district,” one person in the community, who did not want to be identified, said. “These candidates know that they need Satmar support. They know that rank-and-file Satmars will vote like their leaders tell them to.”

Political scientists said the process is not quite that clear-cut, because the chasidic community is a notoriously fractious assemblage of groups with different concerns, and a complicated world to navigate. Still, the individual chasidic groups have high voter turnout and often throw their support behind a single candidate, sometimes generating enough votes to tip a primary or an election in one direction.

Mr. Miller, who is leading his four Democratic challengers in fund-raising but is still lagging in the polls, raised at least $14,000 in Williamsburg, Boro Park, and other parts of Jewish Brooklyn in the past six months and had at least two fund-raising events in private homes during that time. Most of the Miller money, according to records of the Campaign Finance Board, was raised by a consultant named Abe Leichtenstein, and donated in $250 sums by people with Old Testament first names. Mr. Leichtenstein could not be reached for comment.

Mr. Weiner, meanwhile, acknowledged last week that he’d accepted contributions from relatives of an Orthodox rabbi at Boro Park, the dean of the Bais Yaakov Orthodox girls school, who was accused two years ago of misappropriating $700,000. Though Mr. Weiner immediately announced that he was returning the contributions linked to Rabbi Milton Balkany, the incident highlights his already formed relationships within the community.

Some said the Brooklyn-Queens congressman will probably have an edge since he is the sole Jewish candidate in the race and already represents several Jewish neighborhoods in Congress.

Mr. Weiner, who in 1998 defeated Noach Dear, an Orthodox Jew, in the Democratic congressional primary, called the Jewish community his “base” and said his presence there was not part of a campaign strategy.

“This is not an election-year push for me,” he said. “There are other places that I’m trying to grow, but this is my base, these are my constituents.

“I would imagine,” he said, “that it’s like the relationship Freddy Ferrer has with the Puerto Rican community in the Bronx.”

Mr. Miller and Mr. Weiner are not the only candidates reaching out to chasidic rabbis and community leaders.

The Democratic front-runner, Fernando Ferrer, a Hispanic who, in his last bid for mayor, went out of his way to cultivate a strong relationship with Jewish communities, recently hired the head of external affairs at the Metropolitan Council on Jewish Poverty, Kalman Yeger, as executive director of his campaign. Though Mr. Ferrer’s campaign declined to comment for this story, Mr. Yeger is expected to help the former Bronx borough president maintain and strengthen his relationship with the Jewish community.

On Friday, the chairman of the Crown Heights Jewish Community Council, Chanina Sperlin, told The New York Sun that he is scheduled to have lunch with Mr. Ferrer.

“I want to sit down with Fernando Ferrer. We have a personal relationship. We’ve been in touch for the last few years, ” Mr. Sperlin, whose group is a nonprofit Lubavitcher social-service organization, said. “I want to sit down with Gifford Miller. I want to sit down with Anthony Weiner. I want to sit down with all of the candidates. After we sit down with everyone, we’ll make a decision.”

The other candidates on the Democratic side are a Brooklyn council member, Charles Barron, and the borough president of Manhattan, C. Virginia Fields. The Republicans who said they will challenge Mr. Bloomberg in a primary are a former council minority leader, Thomas Ognibene of Queens, and an investment banker from Park Slope, Steven Shaw.

Mr. Sperlin’s group endorsed Mr. Ferrer in the 2001 primary runoff against Mark Green, who is Jewish, and then backed Mr. Bloomberg, who also is Jewish, in the general election. Mr. Sperlin said that he would not rule out endorsing Mr. Bloomberg again, but that it was too soon to decide.

In 2001, Messrs. Ferrer and Green clashed in the Democratic primary campaign over leaflets circulated in mostly Jewish areas of Brooklyn, which had a cartoon lampooning the chummy relationship between Mr. Ferrer and the Reverend Al Sharpton. Mr. Green said his campaign had nothing to do with the leaflets. But the spat ended up causing an ugly division in the Democratic Party that helped Michael Bloomberg win a good chunk of the vote.

With that incident in the past, this year’s candidates seem to be refining their strategies with this community, much as they are with other groups in the city.

The mayor, too, is said to be ramping up his outreach.

No political consultant is suggesting that chasidic and Orthodox Jews will carry any candidate. To earn the mayoralty, the winner will have to attract hundreds of thousands more voters from a wide range of backgrounds.

Mr. Miller’s campaign manager, Brian Hardwick, said the chasidm have the same concerns as most New Yorkers – housing, education, transportation, and jobs – and that the Miller forces do not “target” any group.

“A primary campaign is all about piecing together your support,” he said. “You start with your base and you expand out. And the way you build that support is to address the issues that each community cares about.

“He has been doing that for the last three years in his capacity of speaker,” Mr. Hardwick said of his boss.

A former council member from Brooklyn who represented parts of Williamsburg, Kenneth Fisher, said the Orthodox and chasidic groups can be valuable because they tend to be politically involved and can provide candidates with forums to communicate to secular Jews that they are sensitive to Jewish issues.

“It is not at all surprising that any of the mayor candidates would be looking for support in the chasidic community,” Mr. Fisher, a lawyer who now also works as a lobbyist, said. He added, however, that the Jewish constituencies in Brooklyn range from the modern Orthodox in Brooklyn Heights to the ultra-Orthodox in Boro Park, and that they care about different things. The Satmars, for example, are anti-Zionist, while other groups are intensely concerned with the relationship between America and Israel.

A political consultant who works closely with the Satmar community, Bob Liff, made a similar point.

“There is a perception that you can accomplish a lot through the one-stop shopping approach,” Mr. Liff said, explaining that most rabbis open their doors to any candidate that wants to come through. “But these communities have needs. In Williamsburg, housing is the issue. So essentially, what goes on in these communities is the same thing that goes on in every community in this city.”