The Metro Board, faced with the prospect of signing an agreement it doesn't like with the federal government or closing the subway construction program, voted unanimously yesterday to sign the agreement.

"Our unanimity is based solely on the fact that we need the money," Metro Board Chairman Jerry A. Moore said succinctly. If Metro had not signed, subway construction projects in Maryland, Virginia and the District of Columbia would have ground to halt Sept. 30, the end of the federal fiscal year.

Instead, federal officials have promised, Metro will have $275 million in federal aid so it can continue its program of building the planned 101-mile regional system. Thirty miles are in operation; another 30 are under construction. The new money will provide financing for the first push beyond that 60 miles that already are financed.

Perhaps more important, the agreement means that, for the first time in years, Metro has what the lawyers call "clean hands" in what has been the single most troublesome question separating Metro and federal officials on long-term construction issues. There is now a firm schedule in place for Metro to repay a $1 billion debt incurred as part of the construction program.

The agreement binds Metro to pay one-third of that $1 billion -- plus one third of $2 billion in interest over 30 years -- for the bonds. The federal government, which guaranteed the bonds before they could be sold, will pay the other two-thirds.

Since Metro lacks taxing authority local governments will, in effect, be paying the bill through their contributions to Metro's annual operating deficit, which now exceeds $120 million. If any local government refuses to fund the operating costs, the federal government will simply withhold the federal transit operating assistance that government would normally get under a nationwide program.

The local governments thus are not legally obligated to pay off the bonds -- a posture they had to avoid because of various constitutional or voter-imposed provisions -- but will pay for them anyway because if they do not pay, they will lose federal aid they would otherwise receive. The federal government has a guarantee that Metro will pay its share.

Local Governments are free to continue seeking from Maryland and Virginia legislatures authority to impose special taxes they could earmark for the debt service on the bonds.

With the revenue bond issue thus settled, the question for Metro now becomes one of obtaining administration support for a Metro funding bill that would guarantee completion of the 101-mile system. Local officials wanted to link their signatures on the bond agreement to a pledge of Carter administration support for a full-funding bill that has passed the House and is expected to come up for hearings soon in the Senate. But the federal government had too many cards to play in the form of construction dollars now to be tied to that kind of agreement.

"We're just very pleased" with the Metro action, assistant U.S. Transportation Secretary Mortimer L. Downey said yesterday. Downey said the Carter Administration "will now look at" the question of supporting the funding bill for Metro.

"Where we will come out, I don't know," Downey said. "We still share the goal of completing the 101-mile Metro system."