The Metro board tentatively approved a $456 million operating budget for the next fiscal year yesterday that is designed to hold the line on bus and subway fares and extend rail service on Sundays until midnight.

The budget, which represents a 6.9 percent increase over current costs, largely reflects proposals by Metro General Manager Carmen E. Turner, who has sought to keep down fares to bolster ridership. The board is expected to take final action on the budget next month after a review by local officials.

Under the plan, fares will remain frozen for a third year until mid-1987, Metro's longest stretch without an increase. Fares rose almost annually from 1977 to 1984, when Turner adopted her hold-the-line stand. Minimum rush-hour fares now are set at 80 cents, with higher rates for long trips.

Subway service normally ends at 6 p.m. Sundays, although Metro has frequently kept the rail system open later during holiday periods and for sports and other events. Under the plan, the extended Sunday schedule will take effect July 1, the start of Metro's 1987 fiscal year.

The budget also provides for setting aside $15 million as an initial step in establishing a reserve fund to finance long-term costs of renovating and replacing worn-out subway cars, tracks and other equipment. A recent study warned that these costs are likely to skyrocket in the next 15 years.

Metro officials said that further proposals to offset these expenses, which are expected to exceed $300 million a year by the year 2000, will be drawn up in the next six months.

Gladys W. Mack, a District official who heads the Metro board's budget committee, described the spending plan as "tight" and said it "reflects the emphasis of the board on cost containment."

The budget calls for $229.4 million in subsidies from county and city governments, which rely on real estate and other tax revenues to offset Metro's costs. Metro expects to save $3 million next year because of recent decreases in diesel fuel, heating oil and gasoline costs.

Officials warned that the plan may be jeopardized by the Reagan administration's moves to halt federal operating subsidies for mass transit. If federal subsidies are cut, Metro may have to increase fares, reduce service or seek higher local subsidies, they said. Metro now receives $18.5 million a year in federal operating aid.

In another development, Metro officials proposed expanding bus service in Montgomery County along the developing Colesville Road-Columbia Pike (Rte. 29) corridor. The plan includes changes in bus routes, designated Z, between Silver Spring and residential communities such as Fairland, Greencastle and Colesville. A public hearing is set for April 30.