In a move that stunned and angered city officials, a Senate appropriations panel voted yesterday to slash the federal payment to the District of Columbia to a figure $79 million below what President Carter requested.

Acting on a recommendation by its chairman, Sen. Patrick J. Leahy (D-Vt.), the D.C. Appropriations Subcommittee approved a payment of $238 million as the U.S. government's share of city expenses during the 1979 fiscal year.

The president had supported the city's request for $317 million. The House, in approving its version of the $1.3 billion budget on July 21, approved a payment of $264 million.

Before voting to cut the federal payment, the committee agreed to let the city spend an additional $38.9 million on various city activities - including a new civilian parking enforcement program - that had been disapproved by the House.

Angry reaction at the District Building focused on the cut in the federal payment that, Leahy said, was made possible mainly by forecasts of increased revenue from the city's own local sources. One source is $17.5 million more in parking fines expected under the new enforcement program.

Mayor Walter E. Washington called the payment cut "a crippling blow to critical needs of the city." City Council Chairman Sterling Tucker said the Senate was "taking a giant step backward" as a responsible partner of the city. Marion Barry, chairman of the council's finance and revenue committee, predicted financial chaos.

The three are rivals in the current mayoral campaign.

All of yesterday's actions by the subcommittee are subject to approval by the parent Appropriations Committee and the full Senate, and to agreement with the House.

In addition to its budget actions, the subcommittee approved a proposal by Leahy to impose stiff restrictions on the City Council's participation in the federally funded jobs program authorized by the Comprehensive Employment and Training Act.

Rebuffing pleas from Washington and Tucker not to do so, the subcommittee put a lid of $15,000 on annual CETA salaries and a two-year limit plus other restraints on employment.

A recent Labor Department report found fault with the council's hiring, assignment and pay practices under the CETA program.

At the urging of Sen. Dale Bumpers (D-Ark.), the subcommittee also voted to cut $440,500 from the budget to pressure the city's Transportation Department into adopting the same liberal "right turn on red" rules that are in effect in most states, including Maryland and Virginia.

The city is still awaiting a federal decision on its request to allow turns at red signals only where signs would permit them.

The subcommittee turned down a proposal by the Department of Human Resources that would permit a 5 percent rise in public welfare payments, last increased in 1976.Under the proposal, the average monthly payment to about 30,000 families with dependent children would have risen from $240 to $252.

The subcommittee approved $275,000, denied by the House, for improvements to the city dog pound. And it increased support for the advisory neighborhood commissions from the House-proposed $500,000 to $750,000.

Both Leahy and Sen. Charles McC. Mathias Jr. (R-Md.) said they found the need to oversee the budget of the District's home rule government to be distasteful. But Mathias said it is necessary as long as the city expects a large federal payment.

Mathias voiced a mild protest to Leahy's proposal for yesterday's cut in the payment, but did not try to put any of the money back.

The mayor, talking to reporters, said the payment should be set by some agreed-upon formula at "a stable and predictable figure on a multiple-year basis," to permit orderly financial planning. Both Tucker and Barry have voiced similar views.