D.C. Del. Walter E. Fauntroy, one of the city's most influential Democrats, yesterday endorsed City Council Chairman Sterling Tucker for mayor in next year's elections.

Fauntroys decision was not a surprise. Sources close to the D. C. congressman had been saying for months that Tucker was Fauntroy's preferred mayoral candidate.

Rather, the announcement appeared to be a message to the city's Democrats that the time has come to choose between two popular party members - Tucker and at-large Councilman Marion Barry - who share some similar political bases, but who both want to be mayor.

"I know that the Democrats of the city who have been concerned for unity are divided," Fauntroy said. "I think my actions will at least persuade those that are undecided that just as I cannot vote for two people, neither can they."

For months, Fauntroy and others had been trying to persuade Barry not to run for mayor and instead to seek the Council chairmanship on a Fauntroy-Tucker-Barry slate. Barry, who also had sought Fauntroy's endorsement for mayor, said yesterday that he felt the announcement was designed to place still more pressure on him to abandon that race.

Barry also accused Fauntroy of exerting strong control over Tucker and of trying to be a political boss. "What is rather disturbing is that in reading Congressman. Fauntroy's written statement, it is difficult to figure out who is running for mayor, Mr. Fauntroy or Mr. Tucker," Barry said.

This was a reference to parts of the statement in which Fauntroy had said that if Tucker were to run, Fauntroy would help develop a program for change in city government and sell that program to the voters "so that when the people go to the polls next year they will be voting not for a man, but for a plan to shape up District government . . ."

"A number of us in the District have worked too hard for self-government to allow one person to attempt to dictate the political arrangements in the city," Barry said. He reiterated that he does not plan to run for Council chairman in 1978 and formally will announce his candidacy for mayor early next year.

Tucker, who did not attend Fauntroy's press conference, said he was pleased to receive the endorsement, and considered it "an important building block towards a possible election campaign and an important vote of confidence in my ability to serve." Tucker gave no indication of when he formally would announce his candidacy.

Despite his unannounced status, Tucker already is considered the front-runner for mayor by many city political observers. A Nov. 8 Washington Post survey of 932 voters in six of the city's eight wards found Tucker to be the clear favorite over Barry and Mayor Walter E. Washington among those who voted that day in a school board election.

A major benefit of Fauntroy's endorsement is likely to be the assistance it will give Tucker in putting together a citywide campaign organization, which at this point has been one of the major behind-the-scenes battles taking place between him and Barry, according to several sources.

Fauntroy has won four straight congressional contests and is considered by many to have the best political organization in the city.

Fauntroy, Tucker and Barry all were leaders of the Unity '76 Coalition, which seized control of the D.C. Democratic State Committee last year in elections for positions on the city's Democratic Party steering organization.

During the past several months, both Barry and Tucker have been moving among those who played key roles in the Unity campaign in attempts to recruit key campaign workers for their own political organizations.

Fauntroy's announcement yesterday did not include any mention of who the congressman would support for Council chairman. Sources close to Fauntroy said that in part was a final invitation to Barry to reconsider his plans and accept the chairman's spot.

Fauntroy acknowledged, in fact, that if Barry so decided, "I would just love that."

The lack of an endorsement for chairman also was seen privately by some Fauntroy associates as a result of the considerable problems that are being encountered in efforts of Fauntroy and others to find another feasible candidate besides Barry for the chairman's spot.

The only announced candidate for chairman so far is Councilman Douglas E. Moore, a vigorous opponent of Barry, Tucker and Fauntroy and a frequent political ally of Mayor Washington.Fauntroy has ruled out supporting Moore.

The two principal chairman candidates under consideration by Fauntroy now, according to several well-placed sources, are Councilman Arrington Dixon (D-four) and the Rev. David Eaton, senior minister of All Souls Unitarian Church and a longtime Fauntroy friend.

Several sources said there is concern that Dixon would not be a tough enough campaigner to handle Moore. Eaton would do well against Moore, the sources said, and provide good balance to Tucker's candidacy. But some of Fauntroy's associates fear privately that Eaton might not devote the necessary time and energy to the chairman's job.

Fauntroy said yesterday that he believes "Sterling Tucker will turn District government inside out and right side up." He said Tucker "has been tested and proven at every level in our community, a man equally at ease in the civil rights march as he is in the City Council chamber . . ."

The only announced candidate for mayor next year is John L. Ray, 34, a Democrat and a former congressional lawyer.

Fauntroy made only oblique references to the third major unannounced candidate, Mayor Washington, saying the mayor's administration has been one of "waste and inefficiency."

Fauntroy did not endorse Washington in 1974 - even though Tucker was the mayor's running mate - and was not believed to be giving any serious thought to endorsing Washington in 1978, should the mayor decide to seek re-election.