The Supreme Court yesterday effectively ended a dispute that threatened the financial security of the Metro subway construction budget.

The court left standing a lower court ruling denying Fairfax City's bid to recoup $2 million in subway construction money from Metro and seven Washington area jurisdictions.

"They have fleeced us out of $2 million," groused Fairfax City Mayor Frederick W. Silverthorne when he heard of the court's ruling. He said that the ruling would not place the city under pressure to rejoin the Metro bus system, which it dropped in November 1976, complaining that the transit system was becoming too costly.

While Silverthorne was unhappy with the decision, Metro officials were delighted. Had the ruling gone in Fairfax City's favor, some said they feared it could have established a procedure under which other communities could avoid paying their share of the subway's construction costs.

Fairfax City officials sued Metro in 1977 after it approved an "interim agreement" that failed to contain funding for a planned station at Interstate Rte. 66 and Nutley Road in Vienna that would have served their city.

Metro officials have insisted that the station still might be built, but Silverthorne said yesterday he disagrees. "I believe in God. I believe in Metro," he said. "I suspect I shall see the former before the latter."

The high court made no comment as it declined to hear the city's appeal of a September ruling by the 4th Circuit Court of Appeals The appellate court reversed a ruling by District Judge Oren R. Lewis ordering the $2 million returned to the city on the grounds that Metro's contract with the city had been broken.

Attorneys for both Metro and Fairfax City agreed in separate telephone calls that the Supreme Court's refusal to review the case was the end of the matter.

David Erion, director of technical services for the Northern Virginia Transportation Commission, said officials of both Metro and Fairfax City have been talking privately for about six months over whether the city will rejoin Metro's bus system. "The problem is just working out a cost-sharing arrangement acceptable to both sides," he said I don't know whether the decision will have an effect on that."

In other action, the Supreme Court agreed to hear arguments in the government's appeal of a District of Columbia Court of Appeals decision overturning the conviction of a man identified as the result of an illegal arrest.

The government argued in its brief to the court that the case poses "important and recurring" questions under the Fourth Amendment to the Constitution's requirement of probable cause before a person can be arrested.

The case involves Keith Crews, who was arrested in the vicinity of the Washington Monument, photographed and held for an hour. Police said Crews met the description supplied by three women who had been robbed, over a period of several days, in the women's restroom near the monument.

Crews subsequently was identified from the photograph and then in a line-up by at least one victim. During his trial, however, the judge denied admission of the out-of-court identification but permitted the victims to identify Crews in the courtroom. The D.C. Court of Appeals ruled that Crews' detention for one hour was illegal and that all the subsequent identifications were part of a "causal chain" flowing from that arrest and therefore should not have been permitted at the trial.

The Supreme Court also left standing the 1977 conviction of Peter J. Gianaris for violations of federal gambling laws and the conviction of former Maryland Delegate George J. Santoni (D-Baltimore) for extortion.