The Washington Teachers Union yesterday endorsed City Council member Marion Barry for mayor and the union's president said that about 500 teachers would work telephone banks and campaign door-to-door for Barry this summer.

The teacher's endorsement of Barry is the first crack in the Greater Washington Central Labor Council's attempt at a united labor endorsement for Mayor Walter E. Washington. The council, which claims to represent 150 unions in the Washington area with 200,000 members, pledged its support for the mayor earlier this month even though he was not officially announced for relection.

Teachers union president William H. Simons said the group feels that Barry "offers an opportunity to give new hope to the city." He also said that Barry has over the years been more sympathetic to teacher's salary demands compared to the mayor and the other major candidate in the Sept. 12 Democratic primary, City Council Chairman Sterling Tucker.

"Sterling Tucker ran arm-in-arm with the mayor last time (in 1974) and he's generally supportive of the mayor," said Robert Cobb, a physics teacher at Anacostia High School and chairman of the teacher's union political action committee. "Marion Barry has been more vocally supportive of the school system in pushing for more money."

The teachers' endorsement of Barry came on a voice vote at a meeting attended by about 70 of the union's 5,000 members. A handful of teachers voted against the endorsement

The union, which represents the city's 6,500 elementary and secondary teachers, endorsed Clifford L. Alexander in his losing race against the mayor four years ago. Simons said that about 250 teachers worked for Alexander, but that "we ought to easily double that his time."

"The members have come a long way in understanding the importance of teachers' being involved in the political process," Simons said, noting that when he became president of the group 12 years ago he couldn't get anyone interested in endorsing school board candidates.

Robert Peterson, president of the central labor council, said the teachers' group is "one of the most active unions we have" and that he was disappointed it had deviated from the umbrella group's endorsement of Washington.

David Ryan, president of the Firefighters Association of the District of Columbia, said that many of his union's members also have voiced support for Barry, but that the group will interview all the candidates before making an endorsement.

Both Simons and Ryan criticized the central labor council for making its endorsement without interviewing all the candidates. Petersen said that wasn't necessary because the views and records of the candidates are well known.

Barry said that he couldn't "think of an endorsement that could be more meanful to me."

Tucker had sought the teachers' endorsement and Lee Carty, his deputy campaign manager, said that "obviously we are not overjoyed. We know there are teachers supporting Sterling." The mayor declined comment.