The Senate District Appropriations Subcommittee, at the urging of its new chairman, voted yesterday to cut another $2 million from the federal payment to the D.C. government, dropping the payment to $4 million below the city's request for $20 million.

But the Subcommittee, on its own initiative, added $846,000 to pay the city's share of the $1.8 million Metrorail operating deficit for the current fiscall year.

The District had not asked for the funds, with officials acknowledging this was a play (unsuccessful up to now) to gain support for regional financing under which the suburbs would pay part of the city's large share of the Metro operating costs.

Sen. Patrick J. Leahy (D-Vt.), presiding over the Subcommittee's first decision-making session since he became chairman last month, said the federal payment cut should spur the city to try harder to collect overdue parking tickets and bills from public hospital and clinic patients.

This reflects, he said, "my own brand of fiscal conservatism."

City Council Chairman Sterling Tucker, told later of the Subcommittee actions, reacted with outrage. "I consider this an intrusion on our budget process, which I personally resend," he said. City Budget Director Comer S. Coppie said the actions "must be looked at to see what they mean."

The juggling of the federal payment is an old and confusing game on Capitol Hill. The payment is designed to compensate the city for untaxed federal property. To the extent taxation is not granted, the burden is shifted to local taxpayers.

The maximum amount of the federal payment is authorized by law - $280 million this fiscal year, which ends Sept. 30, and $300 million next fiscal year. Former President Ford originally asked for only $280 million of the latter sum but, at the urging of city officials, President Carter agreed to seek the full $300 million.

Congress already has appropriated $260 million of the $280 million authorized for this year, leaving - in round figures - $20 million still available.

The bill acted upon by the Subcommittee yesterday is a supplemental measure that adds about $40 million in spending to the city's previously approved budget. To help pay for it, the city asked fot the entire $20 million still available from the federal payment.

The House, acting Wednesday on its version of the some bill, granted $18 million. Leahy wanted to cut the figure yeaterday to $15 million. But Sen. Charles McC. Mathias (R-Md.) objected, saying, "I think it's harsh."

"But it's done with a loving concern for the District," Leahy added.

"That's one degree better than benign neglect," Mathias responded, borrowing a phrase made famous by Sen. Daniel P. Moynihan (D-N.Y.) when he was serving as an aide to former President Nixon.

Most of the money in the supplemental bill will go for wage increases for city employees and replenishment of Medicare funds. It is subject to further Senate action and agreement with the House.

The money for Metro does not affect in estimated $13 million needed to pay the District's share of the rail operating subsidy in the next fiscal year, when the system will be expanded by the opening of two newlines. The city has not budgeted those funds, either.