Metro General Manager Richard S. Page proposed yesterday an increase of at least 17 percent in the operating budget for the year beginning July 1. The new budget would require at least one fare increase and would give Washingtonians west of Rock Creek Park their first subway line. It also would be the first time that Metro's operating budget exceeds $300 million.

Page recommended that the fare increase not occur until January 1982, which would be one year after the new, steep raises approved last week are to go into effect. Page conceded that the board may wish to increase fares again next July, as has been the practice.

He said that 85 percent of the Metro budget increase would be uncontrollable if Metro retains current service levels. The other 15 percent represents expansion of subway service in the spring of 1982 from Dupont Circle north under Connecticut Avenue to Van Ness Center, at Connecticut and Yuma Street NW. That long-awaited extension of the Red Line will add two miles to the 37-mile subway system and will open stations at Woodley Park, Cleveland Park and Van Ness Center.

Metro also will begin final testing of the Blue Line extension from National Airport through Alexandria to Huntington in Fairfax County, but that line will not open for passengers until the next year.

Page listed as an option, but did not recommend, expansion of Sunday subway service from eight to 16 hours. That would cost an additional $220,000, Page said, and could be offset with selective reductions in underused bus routes. The board has ignored such suggestions in the past.

Page's budget represents at least a 17.3 percent increase over the $272 million budgeted this year for the combined bus and subway system. The new budget could rise 19.9 percent to $326.5 million if Metro fails to win an adjustment in the labor contract that governs what it must pay its 5,000 bus drivers, subway operators, station attendants and mechanics. That adjustment is one of many unresolved labor issues currently being decided by an arbitrator.

The $326 million figure represents what Page called a "worst-case" budget and assumes that Metro's transit workers will receive four pay increases during the fiscal year, each of which matches the rate of inflation point for point. The assumed rate of inflation is 12 percent. If that happens, Metro officials calculate, the hourly wage for a fully qualified bus driver would jump from the $10.515 it is today to $12.29.

If local and state governments agree to underwrite Page's budget as presented, their share will jump from $110.3 million this year to $135 or $142 million next year, depending on the labor settlement. That would represent an increase of either 22 percent or 29 percent in local support of Metro at a time when local governments are cutting other programs.

Page outlined the budget yesterday for about 130 local officials meeting on Metro problems at Airlie House in Warrenton. Initial reaction was mild, with most officials seeking only information on specific points.

Gladys Mack, a Metro board member who is the District's budget director, said that "considering inflation, this seems to be responsible. I think it's a good job of trying to keep costs under control." The District pays about half of the Metro subsidy and is by far the local partner with the most at stake.

Montgomery County administrator Robert Wilson said he is concerned about any increase in personnel at Metro at a time when "local governments are trying to stabilize the level of employes." Both he and county executive Charles Gilchrist said they need to study the budget more.

Ellen Bosman, a member of the Arlington County Board and a longtime Metro watcher, said, "I don't think Arlington is going to go for a 20 percent increase." She characterized Page's proposal as "not irresponsible, but too big." Arlington's board has been particularly critical of Metro management and has threatened to withhold its January subsidy payment unless Page and the Metro board adopt more cost controls.

In the last year, the Maryland, Virginia and District governments have moved forward on plans to earmark specific non-property tax revenues for Metro operations, so it is impossible to say exactly what the impact of Metro will be on area homeowners' property tax bills.

"We are big and growing at a time when local governments are cutting back" on other programs, Page said at a budget briefing on Wednesday. Given the commitment of the local area to expanding its mass transit capabilities, Page called the budget "a tight but prudent program to serve an estimated 187 million riders . . . ."

About half of Metro's combined bus and subway budget is paid by riders and the federal government has been kicking in $26 million annually as part of a national transit aid program. Page assumes there will be no increase in federal aid. Indeed, early signals from the Reagan administration is that federal assistance for transit operating costs may be cut from current levels.

The Page budget proposed a $609 million program toward completion of the planned 101-mile subway system, the purchase of 50 new buses, the construction of new bus garages in Landover and Springfield, and renovation of the bus system's Northern Garage in the District.