Mayor Marion Barry added $4.5 million to the D.C. public schools' 1982 budget yesterday, apparently staving off further teacher layoffs and putting an end to his long-running feud with the school system over spending policies and financial management.

The mayor's action raises the school spending level for the upcoming school year to $256 million, less than the $265.3 million the Board of Education requested but $18 million more than the mayor originally proposed when he unveiled his 1982 budget last October.

Barry, a vociferous critic of the school board's financial policies, acted after receiving a report from a committee he appointed last month to investigate school spending. The committee found that the public schools have not reduced their staff or cut back on classroom space in step with the dramatic decline in enrollment over the last decade, but it also found that the schools "have experienced a reduction in purchasing power" despite their every-growing budgets.

Barry discussed the report yesteday with the incoming superintendent of schools, Floretta McKenzie, and later proclaimed the start of a "new era" of cooperation instead of confrontation between the city government and the school system. McKenzie, who worked with Barry as acting superintendent when he was president of the school board, responded with praise for the mayor's "sincere effort at making sure our program works well." She said she hoped for a "creative partnership" and a "warm and productive relationship" with the mayor and his staff.

Barry asked the City Council to amend the city's budget for the 1982 fiscal year by removing $4.5 million from the debt service account and transferring it to the schools, which he said he could do by changing the accounting method by which debt service is calculated. In a letter to Council Chairman Arrington Dixon, Barry said the additional school funding "will ensure" that no layoffs will be necessary when classes resume in September.

Last year, budget constraints forced the schools to dismiss 571 teachers, throwing the entire system into disarray and touching off angry exchanges between the mayor and school officials.

Barry sent his proposal to the council expecting it to act today on the amended citywide 1982 budget, but that vote may be deferred because of asnag in Congress over a totally unrelated issue.

Chairman Dixon said he would ask that the vote be postponed, because Rep. Stanford Parris (R-Va.) blocked House action on a bill to raise the annual federal payment to the District by $36.6 million to a total of $336.6 million. The city's 1982 spending plan does not include the extra money, but Barry has said he cannot meet the government's salary or pension obligations without it. Dixon said he wanted to hold up approval of the amended budget until he was sure that the additional federal payment would be forthcoming.

Parris blocked it, a spokesman said, because he is not happy with the District's plans to dump 700 tons of composted sludge a day at Lorton, which is in his congressional district. His refusal to allow the federal payment bill to go to the House floor gives Parris at least three more weeks to consider it, the spokesman said, and it gives the city the same amount of time to respond to the congressman's concerns about the sludge dumping.

Barry said his conciliatory gesture on school funding was "not made lightly.

We don't revise our budget every day." It was done, he told reporters in his office, to help McKenzie at the beginning of her tenure and because "it's better to help children than to argue bout accounting techniques."

The school funding study committee that reported its findings yesterday was headed by city budget director Gladys Mack and included former public school officials who now work for the mayor. They found that nearly half of all school buildings have an enrollment under 70 percent of capacity, the most dramatic example being the nearly new Marie Reed Learning Center in Adams-Morgan, which has a capacity of 1,119 students and an enrollment of 351.

In October 1980, the report said, there were 36,000 vacant seats in the schools, which "cost the public over $12 million." As enrollment dropped from 140,000 in 1972 to an expected 92,100 this September -- a reduction of 34 percent -- the payroll was reduced only 14 percent. Most of that reduction came in the layoffs last year.