Federal and Metro officials reached tentative agreement yesterday on one of the toughest financial problems blocking completion of the planned 100-mile subway system.

The apparent accord establishes a compromise formula for federal and local sharing of a $1 billion debt that Metro owes but that the federal government is committed to pay. Transportation Secretary Brock Adams and Metro board Chairman Joseph S. Wholey announced the compromise yesterday.

Under the tentative agreement, the federal government would pay two-thirds of the interest and principal on the $1 billion. Metro, with help from local or state governments, would pay the remaining third. The entire process would take until the year 2015.

With the agreement, Adams said, he is ready to grant Metro the $275 million in construction money that he had budgeted for fiscal 1979. "I'm willing to go at least $275 million in fiscal 1980," he said.

Adams has withheld the fiscal 1979 money while solutions were sought to several other issues. The $275 million for fiscal 1980 is less than the Metro board wants but more than the federal government has offered to date.

The agreement must be ratified by the full Metro board, but Wholey, who headed the Metro negotiating committee, said yesterday he consulted with a majority of the board members before agreeing to the compromise.

Adams said he must receive final approval from the federal U.S. Office of Management and Budget and, of course, from Congress, but he said he is satisfied that can be achieved.

Two major issues to be decided before final federal approval of Metro's proposed financing plan are some kind of long-range agreement on how local governments will meet Metro operating deficits and details of the construction schedule. The operating deficits have been variously projected to reach as high as $300 million to $500 million by 1990.

The debt, actually $997 million, is owed on five issues of bonds that Metro sold to finance subway construction. The bonds were to be repaid from fares. It was assumed in the planning days of Metro that fares would generate enough income to pay for the operating costs of the subway and to retire the bonds.

The increasing costs of operating transit systems and political unwillingness to increase fares at the same rate as inflation has made those early assumptions false. No public transit system in the United States is breaking even without some kind of taxpayer subsidy, much less by retiring revenue bond issues from fares. Metro collects almost half its bus and subway operating costs in fares. Most of the rest comes from local government budgets.

Metro has been meeting semiannual interest payments on the bonds through a combination of special congressional appropriations and through the use of investment income Metro has earned on unspent construction dollars.

Each of the four payments to date has been made with the federal government contributing 80 percent and Metro 20 percent, a formula that coincides with current federal practice on mass transit capital grants nationwide.

Each payment has been a political crisis. Metro officials have had to lobby Congress hard to come up with the 80 percent. Metro is running out of investment money to pay the 20 percent. At least two local partners of Metro-Alexandria and Prince George's County-have refused to contribute to the revenue bond payments less they create a precedent that would bind them forever. Left unresolved, the issue alone is strong enough to topple Metro's political and financial structure.

If Metro were forced to default on the bond interest payments it would technically be in bankruptcy. The federal government would have to pick up the entire tab, which it has to guarantee before the bond market would touch the Metro bonds. The lawsuits would begin.

Neither side wants such a result. The Metro board, in proposing a financial plan at federal direction in August, suggested that the bonds be retired on an 80 percent federal, 20 percent local basis.

Transportation Sectetary Adams, stating from the outset that he was willing to negotiate, said the federal government would start at 50-50.

There were a series of intense meetings at both the staff and political levels. Negotiations heated up last week and were continued through the weekend. The federal government wanted an answer in time for its proposed 1980 budget, which is nearing completion. Both sides wanted to have a proposalin hand by Friday, when regional officials will meet on Metro questions in Warrenton, Va. Adams is scheduled to speak at that meeting.

Adams and his top aides, including Urban Mass Transportation administrator Richard S. Page, also had the problem of winning OMB approval for any proposal. They told Metro officials during the weekend that the absolute highest the federal government could go would be two-thirds federal, one-third local.

That particular formula has precedent in Metro financing. When local and federal governments originally agreed to build a 98-mile system, the federal share for that system was to be two-thirds. The federal share has since jumped to 80 percent as subsequent Metro appropriations were brought in line with a national transit program. The first estimate on the total Metro construction cost was $2.5 billion. The current estimate for completing the 100-mile system is $7 billion.

Left unanswered is the question of whether local and state jurisdictions will agree to pay the one-third. At least six possible formulas are under consideration, and they involve varying degrees of local and state aid.

Two area councilmen who have strongly questioned Metro's impact on local budgets-Parris N. Glendening of Prince George's County and Donald C. Casey of Alexandria-said yesterday that participation by their localities would depend on the roles their states would play.

"It really doesn't sound unreasonable," Glendening said, "especially if the state makes a big contribution."

"That's only the first hurdle," Casey said. "We has assumed with some justification that the states would take over this program."

The total Metrol bond payment would be about $11.6 million per year until 1986, then would jump to $35 million annually.