Mayor Marion Barry has proposed that the District of Columbia finance its growing share of the cost of operating the Metro bus and subway system by raising faces another 5 cents in 1981 and by earmarking revenues from existing transportation-related taxes.

The mayor's proposal, made available yesterday, was required by Congress as a condition of funding the completion of the planned 101-mile subway system. a

In addition to the fare increase, which would be the second in as many years for D.C. riders, Barry said that some cuts in bus service also would be made. It is also likely that fares will be increased again by Maryland and Virginia next year.

Assuming the D.C. City Council adopts essentially the mayor's proposal, the District will have joined Maryland and Virginia in providing a reliable source of funding to guarantee the continued operation of Metro plus, the payment of the local share of debt service on $1 billion in bonds sold to build the subway.

The proposed fare increase is not technically, a part of the earmarked tax package, the mayor said in a letter to the City Council. But it is a part of the mayor's planned method of meeting future transportation expenses.

Council member Jerry A. Moore Jr. (R-At Large), chairman of the council's Transportation Committee and a member of the Metro board, said in an interview yesterday that he thinks the council will approve the plan after it reconvenes in September.

Moore, a longtime opponent of fare increases, said he was "not anxious to recommend one," but that "it is obvious the District doesn't have any money. It's clear to me we have to resort to the farebox."

A 5-cent increase would raise the minimum District of Columbia rush-hour bus fare from 55 cents to 60 cents. The nonrush-hour fare would rise from 50 cents to 55 cents.

The minimum subway fare in the rush hour is 55 cents, but it increases with the distance of the trip. An increase will have to be negotiated by the District with Maryland and Virginia suburban governments, which have generally been more interested in raising fares than D.C. has been.

According to the mayor's calculations, dedicated tax revenues in the first year would raise $101.5 million, more than enough to cover the District's required obligations. The taxes to be dedicated would be:

The 8 percent sales tax on meals and liquor by the drink.

Motor vehicle registration fees.

The 10-percent room tax.

The 10-cent per gallon gasoline tax, plus the 6 percent gasoline sales tax.

The 1i percent parking sales tax.

Parking meter fees.

Additionally, the mayor said the District will seek congressional approval to reimpose a tax on professionals in the District and use that revenue for Metro-related costs that do not require federally mandated funding guarantee. That tax, previously declared illegal by the courts, is estimated to raise $16 million annually.