The financially pressed District of Columbia government, after weeks of vacillation, yesterday proposed bus fare increases of 5 cents during the rush hour and 10 cents the rest of the time, effective June 29.

The proposals, which will be discussed at Metro Board public hearings in March and April, would represent the first bus fare increase for D.C. riders since a 10-cent increase three years ago.

The proposed increases were forwarded to Metro yesterday by Mayor Marion Barry's transportation director, Douglas N. Schneider. At the same time, however, the D.C. City Council -- traditionally an opponent of fare increases -- sent to committee a resolution to hold the line on D.C. bus fares.

Representatives from both legislative and executive branches agreed yesterday that it was too early to tell whether the fares would, in fact, be increased. It is the first time since the last rise, however, that bus fare increases have actually been advertised for public hearing, the first necessary step in a long process.

Under the proposal, the rush hour bus fare, charged on weekdays between 6 a.m. and 9:30 a.m. and between 3 p.m. and 6:30 p.m. would increase from 50 cents to 55 cents. The fare charged the rest of the time, 40 cents, would be increased to 50 cents.

The basic 40-cent fare for non-rush hours will be 10 years old in June. It is the only fare in Metro's complex bus and subway structure that has remained the same since the Metro takeover of four privately owned bus companies early in 1973.

If both fare increases are adopted as proposed, a total of $3 million in additional revenue would be raised, Schneider estimated yesterday.

The District of Columbia's share of Metro's bus subsidy money is projected to be $57.4 million in the next fiscal year, which begins two days after the proposed fare increase would take place.

Bus fares are technically established by the Metro Board after public hearings. As a practical matter, however, the fares charged on Metrobuses operated within individual jurisdictions are set by the local governments, then referred to Metro for assured ratification.

That is the reason there are widely differing fares for Metrobuses operating in Maryland, Virginia and the District. Maryland and Virginia jurisdictions had submitted their proposed increases to Metro earlier.

All three jurisdictions have agreed to jointly propose two higher fare schedules for the subway. One would increase fares 11 percent and would raise the fare for the shortest rush hour ride from 45 cents to 50 cents. The other would be a 22 percent increase, and would raise the fare for the shortest rush hour ride from 45 cents to 55 cents.

Jerry A. Moore (R-At Large), chairman of the council's Transportation Committee and a member of the Metro Board, is the cosponsor with four other council members of a resolution that would hold the bus fares at their present levels.

"I can't predict what the outcome will be," Moore said, "but my opinion is that at the public hearings people will indicate intense opposition to fare increases."

Joining Moore as cosponsors of the resolution are Hilda Mason (Statehood-At Large), John Ray (D-At Large), Charlene Jarvis (D-Ward 4) and Wilhelmina Rolark (D-Ward 8).

The District of Columbia representatives on the Metro Board have traditionally championed low fares, not only to encourage ridership but also to help the District's many low-income residents.

"We have more low-income residents than any other jurisdiction in this area, and we just have to have a somewhat different philosophy," Moore said in a recent interview. "We can subsidize Metro from other tax sources."

An example of the District's view on this subject is a special fare subsidy that is built into the subway system. All people who enter or exit the subway system at the two D.C. stations east of the Anacostia River -- Minnesota Avenue and Deanwood -- automatically receive a 10-cent reduction, computed by the fare-collecting equipment.