Metro board members, seeking to work their way out of a complex financial and political dilemma, have reached a tentative agreement on a proposal to complete the subway that will require a significant infusion of both federal and local dollars. The Washington Post has learned.

Under the proposal, the total cost of the 100-mile subway system is estimated at $6.6 billion, the highest total even officially projected. At least $2.63 billion in new congressional appropriations and $5.20 million in local funds would be needed.

The plan envisions a two-stage schedule to complete the system. Each stage is a carefully balanced political compromise that gives all of Metro's partners at least some new construction and maintains the integrity of the 100-mile concept on which Metro was first organized.

The two-stage construction schedule is part of a financial plan Metro must present to Transportation Secretary Brock Adams by Aug. 31. Key Metro board members brieted Adams. James T. Mclntyre Jr., director of the Office of Management and Budget, and other ranking federal officials on Wednesday. Federal reaction to the two-stage approach and the rest of the plan was invited before the board formally releases the plan Aug. 17.

"We were impressed with the enormous amount of work and the adroit political skill that went into that [Metro] presentation," a top federal official said. "We are concerned about the numbers."

The two-stage approach is necessary because the final projected cost of Metro far exceeds the federally imposed ceiling of about $5 billion. Metro board members attempted to fit a first stage within the $5 billion limit, and put the second stage beyond that.

They do not quite succeed. Metro has 25 operating miles now and has another 35 miles under construction and fully funded. That 60 miles will cost about $4 billion.

The first stage of the new Metro proposal is estimated to cost $1.4 billion, or $500 million more than the Adams ceiling. That first stage includes:

Completion and operation of the Green Line between the Gallery Place and Anacostia stations (see map).

Completion and operation of the Yellow Line between the L'Enfant Plaza and Pentagon stations.

Completion and operation of the Orange Line between Ballston and Vienna.

Completion and operation of the Yellow Line between the King Street and Van Dorn Street stations.

Substantial construction of the Green-Yellow line between the Fort Totten and Prince George's Plaza stations. Concurrent with that is an agreement between the District of Columbia and Prince George's County that the Green-Yellow line will not be operated north of Gallery Place until it is completed all the way to Green-belt.

Some tunnel construction and track work, but no new operating stations, north of the Silver Spring station on the Glenmont line.

The second stage esentially would be to complete the system, filling in the gaps on the Greenbelt line the Glenmont line te Rosecroft Raceway line and the Franconia-Springfield line. Options would include advance land purchase for possible future routes to Tysons Corner and to Branch Avenue.

"We are not talking about anything less than a 100-mile system and that's what this plan assumes," D.C. Transportation Director Douglas N. Schneider said yesterday. "This is not a recommendation; this is a plan. We want to hear some reaction to it."

The central problem for the Metro board has been devising an approach that would have something for everybody within the $5 billion ceiling (give or take $400 million). That amount of money would exhaust the funds that could be appropriated by Congress from the interstate highway transfer account. Virtually all interstates once planned within the Beltway have been eliminated and the money has been transferred to Metro.

The stage one proposal solves political problems.

In Virginia, it gives Fairfax County and Falls Church some operating railroad. Furthermore, it gets the subway beyond the Ballston station, which makes Arlington County happy. Alexandria and Fairfax County both want the Van Dorn station. All of that can be built relatively cheaply, because it is all at or above ground level.

The opening of the river crossing between the Pentagon and L'Enfant Plaza makes it possible to get trains to the Anacostia-Gallery Place segment, therefore making the District of Columbia happy and shortening by some 10 minutes the trip between the Pentagon and the Southwest office area.

The Anacostia - Gallery Place link gets the Metro into the District's most poorly served and poorest section. "In addition to Anacostia, we get the Archieves, the Waterfront and the Navy Yard." Schneider said. "Plus, our Anacostia riders can transfer directly to the Red Line at Gallery Place."

The construction of the Fort Totten-Prince George's Plaza segment would commit Metro to that corner of the region. Furthermore the construction would be a tunnel under the Fort Totten Park area instead of an elevated railroad, solving a major political problem for D.C. in that neighborhood.

The D.C.-Prince George's agreement commits D.C. to completing its segment from Gallery Place to Fort Totten and commits Prince George's County to completing its segment from Prince George's Plaza to Greenbelt. Furthermore, it eliminates comsideration of Columbia Heights as an interim terminal, something that has been seriously proposed but which presents major traffic, cost and land-use questions.

The additional work on the Glenmont line north of Silver Spring keeps the region committed to that segment, a non-negotiable demand of Montgomery County.

The financial plan, under Adam's direction, also must address the question of how Metro will pay the interest and principal on $1 billion in federally guaranteed revenue bonds already sold for construction. The Metro board is proposing that local governments pay no more than 20 percent of the interest and the federal government at least 80 percent. That percentage formula is the same that would be applied to construction costs generally.

The plan also outlines possible sources of local revenue both to raise the local construction costs and to pay the annual operating deficits, projected to total more than $300 million annually by 1990 for the combined subway and bus systems.

Some elements of the plan may be changed before it is forwarded, but authoritative sources agreed that the central outline is in place. Federal acceptance is quite a different question, however.