D.C. City Councilman Marion Barry, who once stood as a symbol of black anger and frustration in Washington and now has become an ally of the city's powerful white business establishment, said yesterday he will run for mayor next year.

Barry's announcement of his intentions in an interview with The Washington Post set the stage for a mayoral race involving some of the most popular figures in the city's young home-rule government.

Mayor Walter E. Washington, the city's mayor for the past decade, is expected to run for re-election, though he has not yet announced his plans. Another expected, but unannounced, candidate is City Council Chairman Sterling Tucker, who is likely to be endorsed by Del. Walter Fauntroy, believed by many to have the most effective political organization in the city.

For weeks Barry has been under utmost pressure from Fauntroy and other leading city Democrats to head off a possibly devastating spilt in the city's Democratic Party by not challenging Tucker for mayor and instead running for City Council chairman.

But Barry said he has ruled that out. "I don't have any if's, and's or maybe's about this. There's no turning back at this point." Barry said next year, I will formally announce that I am a candidate for mayor, running as a Democrat in a Democratic primary."

Barry's announcement appeared to be aimed at seizing the political initiative from the other two most frequently discussed candidates. Tucker's plans have been clouded by a still-unresloved lawsuit in D.C. Superior Court seeking his removal as Council chairman for alleged violations of the home-rule charter.

Mayor Washington's plans have been stalled in part one confidant said, by an investigation by the U.S. Attorney's office here of bribery allegations involving the mayor's long-time political ally, Joleph P. Yeldell.

"I'm an underdog in this whole situation in the sense that, among many people in the city, there is a feeling that Walter Washington or Sterling Tucker has a better shot than I do," Barry said. "It doesn't mean I can't win. It just means I have to fight a lot of battles.

Barry has been campaigning in a low-key fashion for nearly a year. His statements yesterday, plus recent remarks by some of his closest supporters, appear to indicate that he and his advisers believe their previously unofficial campaign and the political climate in the city have reached a point that allows - or even demands - a more public posture.

One of the principal factors barring Barry from declaring hs candidacy sooner was a provision in the city's election law that would require Barry, whose present Council term expires in 1930, to resign from the Council as soon as he became a candidate for mayor in the 1978 election.

Barry said he has discussed that law with several lawyers, all of whom believe the measure is unconstitutional. Barry said the city's elections board would have to go to court to remove him from office, and even if the constitutionality of the law is upheld, he now believes he is not officially a candidate until his petitions for candidacy are accepted.

Those petitions are not due until next July. By that time, Barry said, he believes the City Council will have passed legislation recently introduced by Arlington Dixon (D-four) that would repeat that section of the election law requiring resignation.

If the restriction is still is effect by Barry said in the interview "I'm prepared to resign my seat."

A second factor that is believed to have delayed Barry's announcement has been the need to determine whether he has a strong enough appeal to various kinds of voters, especially in a contest that would involve Washington and Tucker.

David Abramson, president of the advertising firm of Abramson-Himmelfaro Inc., conducted a survey of 1,000 city residents this summer to ascertain attitudes about city issues and several candidates, including Barry, Tucker and Washington.

Abramson refused to discuss details of the poll's results, which have been shown to Barry. But close Barry supporters say privately that the poll indicates that Barry could get more votes than either Tucker or Mayor Washington if he makes the right kind of appeals to different sectors of the community, some of whom have in the past been considered not to be his strongest supporters.

The emphasis on Barry's image is the key supporters say, because some city businessmen are ever mindful of his dashiki-wearing, militant-talking activist days and want some assurances that he really has changed. For months, in numerous personal appearances with small groups and in his often pro-business chairmanship of the Council's Finance and Revenued Committee. Barry has tried to give those assurances.

In recent weeks, however, the biggest factor has been political, Barry supporters say, in the form of pressure from Fauntroy and others, who said they preferred the 53-year-old Tucker because he was older, more experienced and has served as Council chairman.

On Saturday, Dixon, who is close to both Barry and Tucker, announced that he will support Tucker partially on the basis of experience and urged Barry to run for chairman.

"I reject this notion that order and age and time are the same as ability." the 41-year-old Barry said. "If that's the case, we ought to continue with Walter Washington. He's been in there, he's the present mayor and he's paid his dues."

Barry said he would be hurt "more personally than politically" by Fauntroy's support for Tucker, and said he believes that he already has enough support on the 48-member D.C. Democratic State Committee to block an endorsement of Tucker. "I can say that unequivocally," Barry said.

Although he has not decided on a running mate, Barry said he is giving "serious consideration" to running with a woman, and has already talked to two women, whose names he would not give about running for Council chairman. Neither is a member of the City Council, he said.

"I'm not locking myself into that," Barry said, "except to say that it's time for whoever's running for mayor to give some serious considerations to it."

Barry said he has also discussed a joint candidacy with the Rev. David Eaton, pastor of All Souls Unitarian Church and a close ally of Fauntroy and with Dixon. "I think Sterling has been a good chairman," Barry added, "and I certainly would welcome the opportunity to run with him as my chairman."

Barry said that when his formal announcement is made, he will also propose various programs that his administration would undertake if he is elected. He said he thinks the campaign is likely to cost about $200,000. Ivanhoc Donaldson, Barry's longtime friend and the manager of his 1974 campaign is expected to run Barry's mayoral campaign organization.

Barry was born in Itta Bena, Miss graduated with degrees in chemistry from LeMoyne College in Memphis and Fisk University in Nashville, and come headed the Nashville chapter of the Student Nonviolent Coordinating Committee.

He came to Washington as an organizer for SNCC in 1965, and along with Julius W. Hobson Sr. and Douglas F. Moore he soon becme identified as one of the more militant spokesmen of the city's civil rights and black power movements.

Barry was executive director of Pride, Inc., a self-help organization that boasted of working with street people. With the popularity he gained as Pride, he was elected to the city's school board in 1971. He was elected to an at-large term on the City Council in 1974 and re-elected in 1976. He was recently divorced from his wife of five years, Mary Treadwell Barry. Barry was one of three persons wounded on March 9 when tow armed Hanafi Muslims took over the District Building.