Metro General Manager Richard Page yesterday proposed a $384 million Metro operating budget for fiscal 1984 that he said would improve reliability and expand rail service to Alexandria, but that requires yet another fare increase in 1984.

The budget, 15 percent higher than this year's, is aimed at putting a brake on the growth rate of subsidies from financially pressed area governments and raising the portion of Metro's costs that are covered by fares. Raising fares, however, would have the undesirable effect of helping push Metro's ridership decline into its fourth year.

The Metro board is expected to raise most base fares to 75 cents in April and increase subway mileage fees and some bus zone fees as well. Page's budget, calls for another rise in April 1984that would increase revenues by 6 percent. The board would have to decide exactly what form the increase would take.

Under the new budget, operating subsidies from local and state governments would grow by 16 percent to about $188 million, the slowest growth in three years. But the budget shows that meeting that goal could depend on Metro securing far more federal aid than the Reagan administration is proposing.

"The budget is tight," Page told reporters before presenting it to the Metro board yesterday morning. "It has been cut to below our estimates last September."

Page's budget calls for rail service to be extended south from National Airport to Huntington during the Metro fiscal year, which begins July 1. Yellow Line service linking Gallery Place and National Airport is scheduled to begin this spring. Rail miles would grow as the system expanded and bus miles would be reduced as routes parallel to rail lines were eliminated.

Service would be improved, according to the budget, by arrival of 33 new accordian-sectioned buses as well as new and rebuilt standard-sized buses. Ninety-four new railcars will be delivered during the year. Other new programs would improve bus and rail maintenance standards, reduce employe absenteeism and crack down on theft and fare evasion.

D.C. Mayor Marion Barry immediately condemned the proposal's effect on city finances, telling Page in a letter that he was "dismayed" that D.C.'s projected contribution to Metro would be $8 million more than the $98.5 million in Barry's draft budget for the city.

Suburban officials were less critical in initial comments. Virginia board member John Milliken called the budget "a good faith effort" to reduce costs, but predicted the board would look for more cuts. Board chairman Richard Castaldi of Maryland suggested that assumptions on funding from the federal government and local governments may be too high.

The budget was released at a time when Metro's eight member jurisdictions are pressing more vocally for controls of costs and subsidies. In past months, a consensus has formed among board members that fares must rise sharply, even if they drive more riders away.

Page said that the new budget would reverse a long-standing trend under which fares and other revenues have covered a smaller portion of Metro's total costs each year. Revenues paid 51 percent of Metro's operating expenses in fiscal 1981 but only 45 percent this year.

Page's plan would edge the ratio back up to 46 percent. He also proposed that the board enact official policy that the ratio would never be allowed to slip below 46 percent again.

Reversal of the trend would be made possible largely by extra money from the two fare increases. But the cost, Metro planners acknowledge, would be worsening of Metro's ridership losses. Patronage is expected to be 172 million rides in fiscal 1984. Ridership peaked in fiscal 1980 at 187 million rides and has been on the decline since.

Shortfalls in federal aid could seriously compromise Page's budget. It assumes federal operating aid will total $19.5 million; President Reagan's proposed budget puts the assistance at $6 million, a figure that could force Metro to enact a larger fare increase or bill the local governments for more.

Page's budget assumes total federal aid in 1984, including grants to the rail construction program, will come to $454 million. Reagan's fiscal 1984 budget proposes a program of $305 million.