Several days ago, nearly a year after Anthony A. Williams vanquished three D.C. Council members to win the Democratic mayoral nomination, the mayor had to sit down with one of his supporters in Ward 2 and remind him the campaign was over.

The meeting was requested by council member Jack Evans (D-Ward 2), who came in third in the primary and was the first to extend his hand to the winner. Evans was annoyed that some of Williams's former campaign aides had tried to purge the ward's party organization of Evans loyalists and were treating them as if they were enemies. Evans wanted the mayor to tell his people to chill.

The Ward 2 dust-up may seem insignificant to the success of the District's new team of elected leaders. But this and other incidents--forgetting to invite council member Jim Graham (D-Ward 1) to participate in a mayoral event, a top aide bad-mouthing council member Sharon Ambrose (D-Ward 6) at a public meeting--are the kinds of political peccadilloes that have strained relations between Williams and several members of the council.

In recent weeks, the mayor and council members say, they have grown weary of the sniping and have been working harder to make nice.

"What I'm hearing from people out in the neighborhoods is, 'We want everybody to work together. We don't care about your little feuds,' " Williams said in a recent interview. "I've told our people we have to govern the city now and let's call off all the fighting."

Williams and council members agree cooperation will help speed the process of repairing the District government, which continues to struggle to keep streets clean and safe, improve public schools and attract businesses and residents. Elected officials also say they want to set an example of teamwork for a city that has been shattered by years of divisive politics pitting black residents against white, the middle class against the poor and those who live east of Rock Creek Park against those who dwell west of it.

This summer, Williams has had breakfast with individual council members to talk up a neighborhood improvement program. He now makes sure his aides invite them to mayoral activities held in their wards. And last month, he met with the full council, promising to make such get-togethers routine.

But privately, some Williams aides and supporters still view some council members either as sore losers looking for any reason to criticize the mayor or as busybodies who think they can run D.C. government better.

And several council members sometimes see Williams--who before taking office had lived in the District for only three years--and his aides as cocky winners and know-it-all technocrats who think they don't need help from other elected officials.

Council member Kathy Patterson (D-Ward 3), the only Democratic council member to endorse Williams in the primary, has become one of his most frequent critics. She has challenged some of his personnel decisions, called for an investigation into his campaign finances and sparred with his aides during oversight hearings.

"I think one of the most common hurdles has been the tendency on the part of some of those who work for [Williams] to think they're still in a campaign, where everything is about winning or losing," Patterson said. "If that persists, there'll be a lot of losing."

Williams and Patterson say they still have "a good working relationship." But Patterson, who said she has never blindsided the mayor, said her support does not mean she can't publicly criticize him.

"He's heard it from me first," she said. "Being critical publicly is basically the last thing I would do, but obviously I'm an elected official, and I pledged to work for the voters, and that's what I see myself doing."

Williams said he views most of Patterson's criticism as "exercising her oversight role. . . . She has been supportive in voting on our major initiatives, where it has counted."

The line between genuine policy differences and purely political disagreement often is blurred because four council members--Evans, Harold Brazil (D-At Large), Kevin P. Chavous (D-Ward 7) and Carol Schwartz (R-At Large)--ran against Williams in the primary or general election. All four, who make up a third of the panel, are up for reelection next year.

Williams said he recognizes that the current council is composed of people who are more assertive and independent than past members.

"These are very strong-willed, capable people in this movie," Williams said, including himself in the cast.

But Williams and his aides also said they need space to try some of their ideas about how to improve the government.

"You have to balance communication and consultation at an appropriate level with making decisions and showing leadership," said Max Brown, the mayor's deputy for external affairs. "What the mayor is trying to do is lead the city. . . . Some people will sometimes disagree."

Even though the District's strong-mayor form of government invests the executive branch with authority over city departments, Williams has to go to the council annually to get a budget approved. He also needs at least seven members to support any initiative requiring council approval.

Williams saw the power of a unified council in the spring, when it approved a package of broad tax cuts over his objections. All parties agree that the bruising budget negotiations, which were characterized by tense, closed-door talks and public rhetorical volleys between the mayor on one side and Evans and council member David Catania (R-At Large) on the other, put additional stress on the relationship.

Brazil has struck the most conciliatory posture among the runners-up, saying he respects the voters' decisions. He supported the tax cut but was troubled by the tone of the debate.

"It went beyond where it should have gone. . . . It got nasty and personal," Brazil said. "We still have to work on our relationship with the mayor. It needs to improve significantly."

Of the four council members who ran against Williams, Chavous has the chilliest relationship with the mayor. He represents the ward where the movement to draft Williams was launched. And though he won his ward, which includes middle-class and low-income neighborhoods in Northeast and Southeast Washington, he finished a distant second to Williams in the primary--and was slow to embrace the nominee after the election.

When Williams met with the council last month, Evans and Chavous asked him how he could claim to want to work with them but still allow his supporters to play hardball politics in their wards.

The mayor promised to talk to his people and soon met with Bud Lane, who coordinated his campaign in Ward 2.

"I hope we have sort of come together," said Lane, now chairman of the Ward 2 Democrats, who has been criticized for attempting to shut Evans supporters out of participating in the organization.

"I'm not anti-Jack, I'm just not pro-Jack," he said, adding that he doesn't want to cause unnecessary political trouble for Williams.

"In meetings with the mayor, [Williams] stressed he didn't want a fight with anyone," Lane said. "He has to co-exist with the city council; he didn't need that grief."

CAPTION: D.C. Council members Jack Evans (D-Ward 2), Kathy Patterson (D-Ward 3) and Sharon Ambrose (D-Ward 6) have clashed with the mayor.

CAPTION: Mayor Anthony A. Williams says of the members of the council and himself: "These are very strong-willed, capable people in this movie."