D.C. Democratic mayoral candidate Sterling Tucker yesterday accused Mayor Walter E. Washington of being a "truant and dropout from responsibility" for the city school system's problems and claimed another foe, Councilman Marion Barry, was "over his head" when he was president of the school board.

City Council Chairman Tucker declared that if he is elected mayor he would not "walk away" from the city's problems, as he said the mayor had done. "I want action and accountability, not excuses and red tapes," Tucker said. "The school system cannot continue to be an assembly line for functional illiterates and the mistrained."

Tucker's latest blasts at his two chief rivals came just two weeks before the Sept. 12 Democratic primary at a press conference called to release Tucker's position paper on education, the fifth issue statement he has compiled.

Tucker said that the "D.C. school system is a crime against children." He said, however, that the blame did not lie with the current school board, which he described as "on the whole, good" or Supt. Vincent Reed, whom he said deserved "great credit . . . for pressing the policy of quality education."

Rather, Tucker charged, "the lack of strong, coordinated leadership is the prime reason for the unnecessarily poor state of the school system.

"The present mayor takes the position that the fact the school board is elected precludes his taking any responsibility in education," Tucker said in the position paper. "This is politically expedient. The city's chief executive has a vital, irreplaceable role to play and our children will never get a proper education as long as we have a mayor who is a school dropout."

Tucker alleged that Barry was "indecisive at the helm" as school board president from 1972 to 1974 and that his "flip-flops ushered in an era of needless contention among educators of good will who were trying to operate actively in a policy vacuum."

But the City Council chairman added that "in fairness to Barry, it should be noted that he was over his head in the school board presidency and it was the mayor's obligation discreetly to offer a steadying hand. In the last mayoral election, however, the incumbent campaigned on a platform of silence on the school question."

Tucker's statement did not mention that he ran on the same ticket with the mayor in 1974 or that he sends his 16-year-old daughter, Lauren, to the private Sidwell Friends School.

Tucker said his older daugter, Michele, 28, now a third grade teacher at Sidwell Friends, attended D.C. public schools for several years and received good grades, "but I couldn't determine that she was learning anything.

"I felt I had to do what every parent would do, provide the best possible education for her," Tucker said of the subsequent enrollment of his daughter at Sidwell Friends. But Tucker, a former PTA president, reiterated that he sees improvement of the D.C. public schools "as a priority."

Barry campaign spokeswoman Florence Tate said Tucker's "spurious attempt to dismiss Marion's tenure on the Board of Education as one in which he was 'over his head', is typically elitist and demonstrably false.

"The facts are that during Marion's board presidency he brought order to a badly fractured and chaotic board. His fellow board members thought enough of his management skills and abilities to unprecedentedly elect him president three times," she said.

Mayor Walter E. Washington's campaign manager, Lacy C. Streeter, said that during Washington's administration $329 million had been spent on school buildings and school budgets had increased by 44 percent despite a 10 percent drop in enrollment. In the area of higher education, Streeter said, the budget and enrollment had each increased by more than 1,000 percent during the past 10 years since Washington has been in office.

Tucker said that if he is elected mayor he would create a new position an education coordinator in the mayor's office to organize "total community involvement" in the educational process. "This high-level troubleshooter will make sure the influence and authority of the mayor are tied to the work of the school board, of teachers, of parents and the private sector," he said.

He said that school security, family counseling and health problems would be concerns of the education coordinator "so that teachers are no longer swamped by the community's social problems."

In addition, Tucker said he would ask Supt. Reed for a "five-year plan of school accountability . . . a year-by-year action program to bring D.C. testing results in line with national norms." According to statistics for the 1976-77 school year, the most recent available, the reading performance for D.C. students finishing their senior year of high school was the same as the national average for the start of the 10th grade - a deficit of 2.8 years.

Tucker said the five-year program "will show the public that educators have a specfic, understandable plan, that they are accountable."

While Tucker stopped short of saying that he would seek the firing teachers of classes that fail to improve their test scores, he did say that "when they're not competent there or in any other part of government they ought not be there."