The senate Appropriations Committee, responding to an 11th hour lobbying visit by Mayor Marion Barry voted in effect yesterday to add $10 million to the federal payment to the District of Columbia above what the House had approved only hours earlier.

In a complicated financial maneuver, the Senate committee agreed to add $16.5 million to funding approved by the House. But it then ordered the District to spend $6.5 million of the extra money on an item city officials had not even included in their proposed budget.

The action by the Senate Appropriations Committee is subject to a vote by the full Senate and then to negotiations on a final figure in a joint conference between Senate and House members.

Yesterday's actions by the House and then by the Senate Committee came on the city's request for a $61.8 million supplemental federal payment to help support the city's operations for the rest of the 1980 fiscal year, which ends Sept. 30.

As expected, the House approved $28.8 million, a figure that disappointed Barry. The mayor had hoped for approval of the full amount he had requested to help the city cut costs and increase revenue in order to avert a massive city deficit.

The Senate panel was prepared to reduce the House figures to $25.3 million yesterday, and a draft of its official report reflecting the further $3.5 million reduction already was printed and on the desks of committee members by the time Barry arrived on Capitol Hill.

Before the day was over, he had persuaded Sen. Patrick, J. Leahy (D-Vt.), chairman of the D.C. appropriations subcommittee, to propose an increase to $45.3 million. Leahy did so, and the full committee agreed unanimously.

Of the $16.5 million in added funds, however, Leahy insisted that $6.5 million be spent to pay the city's current share of the costs of the Temporary Commission on Financial Oversight of the District. That joint D.C.-federal body is directing an overhaul of the city's financial management. Barry had not proposed the expenditure.

In its supplemental request, the city had sought funds for an array of programs whose costs had gone beyond the money budgeted earlier in the year -- notably for payroll and energy.

Perhaps the biggest winners in yesterday's Senate panel vote would be the 7,000 people who receive general public assistance from the city. The city pays $180 a month to disabled persons whose applications for permanent support under federal Social Security are being processed.

The House had voted only half the $7 million needed to keep the program running for the rest of the fiscal year. Yesterday's senate vote would restore the full amount.

The Senate vote left alive a threat that the D.C. Superior Court may have to shut down virtually all its operations perhaps starting as early as next month, until the start of the 1981 fiscal year on Oct. 1. The appropriations panel did not respond to a warning by the court's chief judge, H. Carl Moultrie I, that it needed $1.2 million in added witness and juror fees to maintain operations.

The federal payment, the central issue in the District supplemental budget, is the annual sum appropriated by Congress to pay the U.S. share of city operations. It is intended to reimburse the city for taxes it cannot collect on federal and foreign embassy property, and for unusual expenses the city incurs because it is the nation's capital.

The payment is authorized by the city's Home Rule Act to go as high as $300 million. Congress, when it passed the city's basic 1980 budget last year, approved only $238.2 million of the sum. In submitting the supplemental request, Barry asked for the full remaining $61.8 million, only to see the figure scaled down yesterday by both the House and the Senate committee.

If Congress finally agrees on the figure adopted yesterday by the Senate panel, the total federal payment for the year would reach $283.5 million, a record high.

The extra $16.5 million voted by the Senate panel for the federal payment was made possible by reshuffling various city fund accounts. Barry proposed, and Sen. Leahy agreed, to reduce the city's spending on capital construction projects by $20 million on order to divert money into day-to-day operations.

Leahy said Barry had promised to supply a list of the construction projects that would be delayed.