Mayor Marion Barry, whom D.C. school board members just weeks ago were calling "public enemy number one of public education," declared a new era of cooperation yesterday between himself and the board, which is now headed by a man Barry endorsed for election.

Barry, who proposed severe budget cuts for the schools this year, pledged an end to the acrimony that has marked his relations with the board over the last two years after meeting for an hour with the newly elected board president, Eugene Kinlow (at-large), and Bettie G. Benjamin (Ward 5), the new vice president.

"I'm sure there's going to be a little bit of institutional stress from time to time. But the kind of acrimony we think we've seen in the past will not exist," Kinklow said.

"The past is the past," Barry said. "I stand ready to do all I can as mayor to offer support" to the board.

Barry, himself a former school board president, would not say whether what he termed the "new era of cooperation" would result in more funding for the school system. This year Barry reduced the school budget by $35 million, leading to the layoffs of more than 700 teachers and several program reductions, including some industrial arts, music and adult education.

And despite his pledges of support for the school board, which is theoretically an independent arm of city government, Barry said he would be seeking candidates to support in next November's school board election.

Five board members -- Carol Schwartz (Ward 3), Alaire B. Rieffel (Ward 2), Barbara Lett Simmons (at-large), R. Calvin Lockridge (Ward 8) and Frank Shaffer-Corona (at-large), some of Barry's harshest critics in the past -- are up for reelection.

"I'm not going to sit on the sidelines," Barry said.

Lockridge said he felt there were political motives underlying Barry's new cooperative posture. "I think the major wants better relations with the board because it's getting closer to election time," Lockridge said. "We could have put Shaffer-Corona (the only school board member ever to be censured by his colleagues) as president, and the mayor would have been trying to make better relations."

Ongoing political squabbles between Barry and the board have been cited by many citizens as one of the deterents to better education in the city's troubled public schools.

Barry, frustrated in his past attempts to win influence on the 11-member board, threw his political weight behind six candidates in the 1979 elections, four of whom won, including Kinlow. But the other three -- Linda Cropp (Ward 4), Nathaniel Bush (Ward 7) and Frank Smith (Ward 1) did not vote for Kinlow in this week's election for board president. (

The coming together of Barry and the new board leadership occurs at a time when the board is seeking a relacement for Vincent E. Reed, who retired after what is generally viewed as five stabilizing years as school superintendent. Reed alleged problems with the board, particularly its interference in day-to-day school operations, when he announced his retirement. i

The new majority that made Kinlow board president has indicated that they wold seek a new superintendent who believed that the board, not the superintendent, should have the upper hand in setting school policy and directing operations.

The mayor said yesterday that he would send the board the names of persons who might be chosen as the new superintendent.

He also said he wants his staff to work more closely with school officials on special projects. One such project, he said, would be the use by various city agencies of space in school buildings. In the past, the mayor has proposed closing schools with low enrollments and selling the property to raise funds for the city coffers -- a move the board has vehemently opposed.

Despite his assertion that he is not yet ready to declare his support of any school board candidate, Barry talked this week with Athel Q. Liggins, principal of McKinley High School in Northeast Washington, about the possibility of Liggins seeking an at-large seat on the board if he retires from the system this year.

Another potential candidate for Barry's support is Mary Ann Keeffe, former chairman of the Ward 3 Democratic Club. Keeffe said she is willing to challenge Schwartz, a Republican who won two-thirds of the vote in 1977. Keeffe said, however, that she has not yet talked with the mayor about an endorsement.

Dwight S. Cropp, Barry's executive secretary, the former executive secretary to the school board and the husband of board member Linda Cropp, said, "A large segment of the citizenry expect the mayor to exert some influence on the schools. The mayor is being held accountable for the ills of the system, and is interested in supporting responsible and substantive people for the school board."