The House District Committee yesterday supported President Reagan's proposal for an increase of $19.5 million in the federal payment to the District, but rejected his staff's recommendation that $20 million in prison construction funds be drawn from the payment.

The total federal payment would be $444.5 million, reflecting the first increase in two years. The prison funds, proposed as a separate line item last fall by Sen. Arlen Specter (R-Pa.), would come in addition to the federal payment. The Office of Management and Budget had recommended that the prison funds be considered part of the federal payment, which would have represented a net loss of $20 million to the city.

Wilhelmina W. Marshall, a spokeswoman for the mayor's budget office, said that the District Committee's action "is a positive step toward getting favorable consideration for the increase through the whole committee process."

The federal payment makes up about 20 percent of the city's annual budget. A portion of the proposed $19.5 million federal payment increase could be offset by a proposed increase in the city's contribution for employes covered by the federal retirement system, which could cost $10 million. In addition, a proposed increase in contributions toward health benefit costs for retirees would cost the city $8 million.