The Greater Washington Central Labor Council, the largest umbrella group of labor organizations in the city, has formally urged Mayor Walter E. Washington to run for reelection and given the mayor its advance endorsement.

The council, which claims to represent more than 100 unions and about 125,000 people in the metropolitan area (most of them in the District), voted 70 to 14 Monday night to back the mayor, according to Ron Richardson, executive secretary-treasurer of the Hotel and Restaurant Employees Union Local 25.

"For the last 10 years, the mayor has been practically the only person in city government who has been completely responsive to labor people," Richardson said yesterday. "By and large, his track record has been excellent."

Richardson specifically mentioned the mayor's selection of labor representatives to serve on various city boards and commissions, and the city's high minimum wage and high level of workers compensation payments. He also cited an unsuccessful effort by the mayor to raise the gross receipts tax on business, which, Richardson

The mayor, who is expected to announce his candidacy for election to a second four-year term within the next two weeks, said through a spokesman, "I appreciate this additional significant expression of confidence."

The endorsement, which came as no surprise to many political observers in the city, means that many of the individual unions can be counted on to make financial contributions to the mayor's anticipated candidacy, and also provide workers, mailing lists and other support.

The Central Labor Council endorsed the mayor in his 1974 race against lawyer Clifford L. Alexander. Of nearly $196,000 in reported campaign contributions received by the mayor in 1974, more than $27,000 came from labor organizations or persons clearly identified with organized labor, according to campaign finance reports.

In the still unwritten rules of fledgling home-rule politics, however, it is not always clear how great an impact the labor endorsement has.

In 1976, for example, labor and the mayor backed the Open Party slate in the contest for control of the city's Democratic party organization. The Open Party won only three of the 44 seats at stake, however, losing to the Unity '76 Coalition put together by the mayor's two principal rivals in this fall's contest, City Council Chairman Sterling Tucker and Council member Marion Barry.

Tucker was unavailable for comment yesterday on the endorsement but had said earlier that he expected the labor group to support the mayor. "But I'm going to get a large number of the rank and file's votes," he predicted.

Barry said that he, too, expects to get votes from individual union members. "On every front he (the mayor) hasn't been there," Barry said. "Maybe the leadership is out of touch with the membership. Who knows?"

Richarson said that the Mayor opposition to the endorsement came from two groups - the Washington Teachers Union, which represents the city's 6,300 public elementary and secondary schoolteachers' and the Firefighters Association of the District of Columbia, which represents most of the city's 1,400 firemen.

Both the teachers and firemen had informally expressed support for Barry, who last year carried out a political end run on the mayor by separately negotiating a pay raise for teachers, firemen and police, equal to the cost-of-living increases given most other city employes.

In the past, these groups sometimes had received pay raises later than other employes, and on occasion had blamed the mayor for it. The pact negotiated by Barry lessened any delay.