D.C. school and city government officials said yesterday they have found the money to avert a scheduled six-day furlough of 8,800 school employes in September and finish the current fiscal year for the school system in the black.

The school board last month approved the furlough to avoid a projected $4.8 million budget deficit. But yesterday, D.C. budget director Gladys W. Mack said she had found a way of adding $2.8 million to the current year's budget. She would not disclose where the money was found.

In addition, school board member R. Calvin Lockridge (Ward 8), chairman of the board's finance committee, said the school system can make up the rest of the deficit by postponing $2 million in building repairs and purchases of supplies such as pencils, pads and other equipment used mostly in the system's administrative offices.

Mack's efforts to find the extra funds were seen by some District Building observers as a move to mute the clamor of the city's 5,300 teachers, angry over the scheduled furlough and the layoffs of about 400 teachers last year. The influential Washington Teachers Union supported Barry in the last mayoral election, and potential contenders in next year's election already are starting to jockey for union favor.

The mayor's office refused yesterday to say whether Barry will authorize the transfer of funds to the school budget, but he is expected to announce such a move at an ll:30 a.m press conference today.

Mack said in a letter sent to School Board President Eugene Kinlow this week that the mayor had directed her to find an "acceptable solution to the furlough issue." But she refused to disclose the source of the additional funds.

In an interview, she said only that they are not part of the $7 million surplus in tax revenues the city recently discovered it has.

Mack added that she would not recommend that the mayor transfer the $2.8 million to the school budget unless the school system agrees to two terms: that it not overspend its fiscal l982 budget and pay the District of Columbia about $500,000 a year each year for helping to administer some of the federal grants the schools receive.

Lockridge said a letter was being drafted yesterday afternoon, informing Mack that the schools would agree to those terms. "We have never overspent a budget, even when we were constantly having money stolen from us," Lockridge said, referring to the reductions the mayor and City Council have made to the school budgets over the last two years.