The D.C. City Council approved yesterday a stopgap transfer of funds sought by Mayor Marion Barry to get his summer jobs program fully under way, but refused to support a second funding shuffle that Barry proposed to keep from overspending the city budget.

The transfer of $2.5 million for summer employment was not controversial, but the second transfer -- up to $4 million of school funds to other agencies -- put the major and the council on opposite sides of an educational financing issue that must be settled by Congress.

The council rushed through its backing for a $2.5 million loan from one city fund to another to permit 8,564 youngsters to go onto summer payroll next Monday. Funds for 22,000 other jobs previously had been approved.

The shift still must be approved by the two congressional subcommittees on District of Columbia appropriations -- a formality, since the two subcommittee chairmen already have promised to grant it. The money is to be paid in mid-July after Congress approves a noncontroversial $7.3 million appropriation to pay for the jobs program for the entire summer.

The second proposed juggling of city funds involves $4 million of the nearly $9 million that the school system saved in operating costs because of the 23-day strike by teachers in March.

The school board has asked Congress to let it spend the $9 million on several educational programs, including $3.5 million for textbooks and equipment, $1 million for improved building maintenance and $600,000 for contracts to provide private schooling for handicapped pupils.

Barry said he wanted to see $4 million of the money used in another way that would, in effect take it away from the schools.

Faced with a $4 million shortage in funds voted by the Senate to pay employers of all city agencies for the rest of the fiscal year, which ends Sept. 30 Barry urged that the entire amount be taken out of the school budget.

The alternative, he said, is overspending by several city agencies that would put them into the red at the end of the fiscal year, a matter that would be "serious for the fiscal health of the city."

The major is permitted to comment on requests made to Congress by the school board to transfer previously appropriated funds, but has no power to enforce his position. Yesterday he asked the council to support him.

Council member Betty Ann Kane (D-At Large), a former finance chairman of the school board, and Hilda Mason (Statehood-At Large), a former school board member, led opposition yesterday to the major's proposal. Kane's motion of support for the school board's request was approved by an apparently unanimous voice vote.

Council member John A. Wilson (D-Ward 2) remained absent yesterday. Members of his staff said he has stayed out of touch with them since threatening on June 25 to resign his council seat.