The 1982 campaign for mayor of the District of Columbia is under way, and former mayor Walter E. Washington, grinning but tight-lipped about his intentions, is holding the first trump card -- close to his vest.

One by one, the expected challengers to Mayor Marion Barry have been courting Washington during these not-so-steamy days of August -- at lunch, at poolside parties, on the telephone. Each is hoping to pick up early campaign support form the man who received about one-third of the Democratic vote in 1978 and is not expected to run next year.

"I haven't made any commitments, but I am talking to people," Washington, now a lawyer in private practice who has remained on the edge of city politics, said yesterday.

Former City Council chairman Sterling Tucker, a narrow loser in a close three-way Democratic primary in 1978, met with about a dozen of Washington's loyal supporters Wednesday night to try to line up support for his still unannounced but firmly expected candidacy. No commitments were made, according to several who attended the meeting.

And yesterday, council member John Ray (D-At Large) announced formation of a campaign "exploratory committee" that included the names of two erstwhile Washington stalwarts, former Democratic National Committeewoman and Ward 5 activist Lillian Huff and the Rev. A Knighton Stanley of Peoples Congregational Church.

Ray and Tucker have been the most active would-be challengers to Barry, who, as the incumbent, is considered the early favorite by many political observers. But with just over a year remaining until the crucial Democratic primary, many perennial and not-so-perennial names are making the rounds in city political circles.

Former Health and Human Services Secretary Patricia Harris says she has been approached by several people, but she only laughed yesterday when asked by a reporter if she would be running.

Former school superintendent Vincent E. Reed, now an assistant secretary of education, is being chatted about by some city businessmen, according to several sources.

City Council member Betty Ann Kane (D-At-Large) has taken a poll that she says proves the mayor needn't be black, though many expect her to more likely run for chairman of the City Council.

Former Secretary of the Army Clifford L. Alexander, an unsuccessful contender in 1974, is still mentioned by some, but many insiders consider an Alexander candidancy a long shot at best.

The late summer political maneuvering stems from a widespread perception that Barry, winner of the 1978 primary with only 35 percent of the vote and unsuccessfuly in many of his attempts to broaden his base, is vulnerable.

Some of the potential contenders try to portray him as a mayor whose stewardship has led to an increase in crime, a major municipal money crisis and a city government out of control. The mayor's high-profile attack on drug trafficking and his recent increase in funds for the public schools are efforts to clean up his image, they say.

Several polls, including one taken by Kane, have found Barry with even less support now among Democrats than in 1978.

"He's read the polls . . . and he's going to try to do what he can to bring it [his standing in them] up," said one lawyer involved in city politics.

Barry has all but declared his candidacy, but has not been one of those seeking support from Washington at this point. Instead, according to several sources, he has tried to first solidify his own base.

The mayor met last week for more than two hours with Ray and Councilman John A. Wilson (D-Ward 2), who also has been mentioned as a possible contender for mayor.

Ray, who acknowledged that the meeting took place and that "it was not the first time," said that the mayor asked for the meeting. "It was an open discussion on what people are going to do," said Ray. He said he told the mayor he was going to set up the exploratory committee.

Ray was a long-shot candidate for mayor in 1978, but abandoned his candidacy and endorsed Barry in the final days before the Democratic primary. Barry in turn endorsed Ray in the May 1, 1979, special election to complete Barry's unexpired term as an at-large council member. Ray was elected in his own right in 1980.

Over the last three years, Ray has siphoned off many key political operatives from the Barry organization, and that was apparent yesterday when Ray announced formation of an exploratory committee that he expects to raise $50,000 by early October.

The committee will be headed by Joseph B. Carter, a vice president of Garfinckel's who served as chairman of Barry's strategy committee in 1978. Carter said yesterday he had abandoned his support for Barry because he was disappointed in the mayor's policies toward the poor and the elderly, thought Barry was "playing politics with the teachers" and because the mayor had declined this year to lower the city's property tax rate.

A key fundraiser for the exploratory committee will be Nancy McElroy Folger of Cleveland Park, who was a early organizer and fund-raiser for Barry in 1978, and resigned Wednesday as a member of Ray's Council staff in order to work full time on the potential campaign.

Folger said yesterday that she felt about $500,000 would have to be raised to finance a successful campaign against Barry. Ray is known to feel that raising considerable funds quickley is crucial to proving that he is a viable candidate.

Another member of the committee is consumer activiist Ann Brown, who was cochairman of Tucker's 1978 campaign.

Tucker declined to talk about Wednesday night's meeting, which took place at the Upshur Street NW home of Charles T. Duncan, the former D. C. corporation counsel and a longtime confident of former mayor Washington.

Among those attending were former Office of Human Rights director James Baldwin, who ran H.R. Crawford's successful City Council campaign in Ward 7 last year; realtor Flaxie Pinkett, a longtime associate of Washington's, Georgetown businesssman A. L. Wheeler, lawyer James l. Hudson, vice chairman of Washington's '78 bid, and attorney William Borders.

Also at the meeting were Emily Y. Washington, who has run unsuccessfully for the school board and the City Council, and Charlotte Chapman, who served as treasurer of Walter Washington's 1978 campaign.

Tucker's basic pitch, according to sources, is that the city is in trouble financially and that Barry does not have the administrative skills to run the city. The sources said Tucker had charts with statistics showing that he lost by one 1,500 votes last time, arguing that Barry was far less popular than either Tucker or Washington.

"His thrust was simple arithmetic," said one person who attended the meeting. "If the people who voted for him in 1978 and the people who voted for the mayor (Washington) in '78 had only one of the two candidates to vote for, he thinks either one would have won. Well, that's no secret.

"Because he intends to run and because he has had three years to watch the situation . . . he feels if he can get the strong supporters of Walter Washington to support him, that will turn the tide to him . . . This is not a bad deduction."

Tucker, who said he expects to make a decision on his possible campaign by late November or early December, declined in a telephone interview yesterday to discuss other potential candidates, but did take a swipe at Barry's often touted 13-point anti-crime program.

"The center point of the mayor's crime program is the police playing musical str5eets with the prostitutes," Tucker said.

Harris said yesterday that several persons whom she would not name had approached her about running for mayor. But she is not likely to be a candidate, she said."I keep laughing at them. I am enormously flattered but, who needs it?"