The Montgomery County Council voted yesterday to approve a stopgap financing plan for continued work on the Metrorail system, following similar action late Monday night by the Falls Church City Council.

The stopgap plan is designed to stretch all available and potential funds, a total of $942.8 million, to complete 60 miles of rail routes while the fate of the full 100-mile system is being determined politically.

Although three other local governments still must approve the financing plan to put it into effect, there appear to be no major policy problems standing in the way of their approval.

One of those governments is the District of Columbia.A spokesman for the major's office said the agreement document is still being reviewed by legal officers, but that there appear to be no objections to it.

The other governments still to act on the stopgap plan are Alexandria and Prince George's County.

Area officials are working on plans that hope will result in the adoption of a permanent financial plan later this year, to complete as much as possible of the planned 100-mile system.n the interim, however, Metro needed some kind of formal agreement to continue work. Such a plan was submitted to the Metro Board and approved on Dec. 2.

It would provide funds to complete and start operating six routes from downtown Washington to Huntington and Glebe Road stations in Virginia and to the Shady Grove, Silver Spring, New Carrollton and Addison Road stations in Maryland.

Because the stopgap plan omitted the westward extension of the line from Glebe Road to Vienna, the Fairfax City government filed suit against Metro - and against all seven other local jurisdictions involved in Metro - in an attempt to block the plan's execution. Fairfax City already has paid all it expects to owe for Metro, so it is not a party to the new agreement.

Fairfax City's case is scheduled for trial next Tuesday in U.S. District Court in Alexandria.

The lawsuit led some governments, including Alexandria which otherwise supports it, from the stopgap plan. Falls Church feared, as did Fairfax City, that it might never get Metro service as the result of the omission of the Vienna line from the stopgap plan.

On Monday night, the Falls Church Council reversed itself, agreeing that completion of the Glebe Road line offers hope for the Vienna extension.

Council member John Enright insisted, however, that the city tie its support toan insistence that the line be completed all the way to Vienna, and not be cut short at either the East Falls Church or West Falls Church stations.

The possiblity of ending the line at West Falls Church station is being considered as part of a system-wide study of Metro completion.

"This would be disastrous for the city of Falls Church," Enright told his colleagues. The Council's resolution contains language embracing Enright's views.

Another type of problem occurred in suburban Maryland. Since the stopgap plan stresses construction in Montgomery County more than Prince George's, officials of Prince George's protested that their neighbors were getting more state funds.

The state has earmarked a total of $160.9 million for metrorail construction. After the stopgap plan is carried out, only $29 million will remain.

After negotiations, which concluded yesterday with the Montgomery County Council's approval the two counties agreed that Prince George's can expect ultimately to get the benefit of that $29 million.

The plan was not presented to the Prince George's Council which is not expected to have objections.