Mayor Marion Barry and the D.C. City Council fought for a while yesterday over the power to shift funds in the city budget with the future of 63 City Council employees hanging in the balance.

But at noon, Barry agreed to sign an agreement to provide interim funding for the 63, who otherwise would have lost their jobs, until the city's budget for the fiscal year beginning Monday is passed by Congress. That passage is likely to come well after Monday.

The battle came in the wake of the council's overwhelming vote last week to impose tighter restrictions on Barry's authority to transfer city funds from one budget to another. By a lopsided vote, the council required notice of any shift in funds. Previously, Barry could shift up to $25,000 without notifying the council.

An angry Barry had promised not to sign the law because it would "tie my hand." When the council later had to come to the mayor to obtain interim funds for the council employees, Barry pressed for a change in the council's attitude, sources said. But the council members refused, and Barry gave in.

Most of the 63 formerly were paid with funds under the U.S. Comprehensive Employment and Training Act, (CETA), but that funding ran out in March and they were transferred to the regular city payroll.

A March 29 agreement, which Council Chairman Arrington Dixon never signed, would have provided more than $350,000 to pay those salaries until Oct. 1, when the city expected to receive permanent funds in the fiscal 1980 budget. An amended agreement signed yesterday by Barry and Dixon would provide funding until whatever date Congress passes the fiscal 1980 budget bill.