D.C. Mayor Marion Barry informed school officials yesterday that he would not seek the additional funds the school system has said it needs to stave off an anticipated $20 million deficit in this year's school budget.

Instead, Barry reiterated that he expects the school system to trim $6 million from its $247 million budget for fiscal 1980.

"In these days of declining student enrollment, the board is asked to adjust to today's fiscal realities, just as D.C. agencies are asked to make even greater sacrifices than asked to our public school system," Barry said.

Barry has ordered cuts in several city agencies to prevent a citywide budget shortfall that could reach as much as $172 million.

The mayor's action is the latest in the tug of war between Barry and the school system. The school board has so far refused to honor Barry's order for a budget cutback, citing a 1978 Superior Court ruling that prohibits the mayor from withholding funds from the school system after they have been appropriated by Congress.

On Monday, Corporation Counsel Judith Rogers issued an opinion which supported Barry's position that he has the authority to order across-the-board reductions in spending among city agencies to prevent a general, citywide shortfall.

But John E. Warren, chairman of the school board committee that handles budget matters, said he would not accept Rogers' opinion, and that "a majority of the board" would be prepared to go to court to prevent Barry from changing the school's budget.

Warren and other board members, meanwhile, have been meeting during the week to decide how they can juggle the current year's budget so that the school system will be able to pay heavy costs for fuel and special education programs and employes' salaries.

After a meeting Monday, members of the Finance Committee said they thought they had found ways of accounting for the $20 million deficit without eliminating any existing programs. But if that plan were put into effect, Warren said he later learned, the school system would wind up at the end of the year without enough funds to pay substitute teachers' salaries.

In addition, the board committee was counting on getting $8 million more from Congress. The plan also did not take in account Barry's order to cut $6 million.

Warren's committee has asked Superintendent Vincent Reed's staff to submit proposals of what current educational programs could be cut if sacrifices have to be made.

Warren also asserted that the school board, despite Barry's order, could still go directly to Congress to ask for additional funds.

The school board, Warren said, is awaiting a printout from the city's financial management system that would show how much money the school system has spent, and how much of its 1980 appropriation remains.