Mayor Marion Barry and members of the D.C. school board agreed last night to explore a possible change in the handling of educational funds that could help reduce the constant haggling between City Hall and school officials.

Under the proposal, to be explored by a special task force, the school system would gain full control of its money for the entire year once it is appropriated by Congress. It would replace a procedure under which City Hall now keeps the money and is supposed to pay the bills when school officials submit the necessary vouchers.

Even though it does not issue the checks, the school board now has full autonomy over deciding on the spending patterns.

School officials have complained that bills sometimes are not paid because of slip-ups in the system or disputes with the city over how much money actually is available.

Barry and R. Calvin Lockridge, school board president, announced the agreement on setting up a task force after a 2 1/2-hour closed meeting between the mayor and the board members in the mayor's conference room.

Barry also said the task force would explore long-term school financing, including a highly tentative possibility that the school board might be permitted in the future to levy its own taxes instead of relying on the city treasury.

Relations between the school board and the mayor -- himself a former school board president -- have been badly strained recently because of budget cuts imposed by Barry.

Lockridge said the mayor had more bad news for school officials at the meeting: the school system will be forced to cut $20 million from its $252 million proposed budget for the 1981 fiscal year that is now pending before Congress.