The Reagan administration has agreed to recommend a $25 million increase in the federal payment to the District of Columbia for fiscal 1984, or an increase of about 7 percent over the record $361 million federal payment that Congress had approved for this fiscal year, according to congressional and city government sources.

The payment, which would total $386 million next year if the Reagan proposal is approved by Congress, is in lieu of taxes to compensate the city government for the services it provides to the federal government.

But the increase, which had been sought by Mayor Marion Barry, could be offset if the federal Office of Management and Budget (OMB) persuades the president to seek a significant increase in the city's share of the operating cost of St. Elizabeths Hospital.

A similar effort by OMB was rejected by Congress last year.

The city currently provides 17 to 22 percent of the hospital's $128.4 million annual operating budget, to defray the cost of treating patients who live in the District.

OMB wants the city to more than double its contribution to about $60 million.

City Administrator Elijah B. Rogers said yesterday that he could not comment on the new federal payment proposal until the president transmits his 1984 budget proposal to Congress on Jan. 31.

That budget will be for the fiscal year that begins next Oct. 1.

But Rogers said that the city has not agreed to tie any increase in the federal payment to an increase in the city's share of St. Elizabeths' operating costs.

"There's no understanding or agreement at all," he said.

On a separate financial issue with long-term implications for the city, Rogers said that the city government would attempt to enter the private bond market this summer for the first time, in an effort to reduce its reliance on the U.S. Treasury to finance capital improvements.

D.C. officials believe that they can reduce the city's interest payments on long-term borrowing by using private sources, rather than the federal government.

Moreover, the Treasury Department has said that it wants to end its policy of making long-term loans to the District within two years.

"We plan to test the bond market, hopefully this summer," Rogers said. "We are confident we can get a decent [bond] rating, so our long-term payments would be less."