After two years of trying to make it fly, the Alexandria City Council yesterday grounded a plan to build the Washington area's first public heliport.

The $2.2 million heliport was backed by the Federal Aviation Administration and sponsored by former mayor Charles E. Beatley. It was touted as a forward-looking project to fly passengers to Dulles International Airport and executives to New York City.

But James P. Moran Jr., who defeated Beatley last May, scoffed at the need to land helicopters, and City Manager Vola Lawson warned that it could be a troublesome liability.

"It was a fringe luxury that would have become more trouble than it would have been worth," Moran said yesterday.

By unanimously voting yesterday to withdraw a request for an FAA environmental impact study on the heliport, the council effectively killed the project.

The 45,000-square-foot heliport was to have been located near the Eisenhower Avenue Metrorail station, and federal and state funds would have paid 95 percent of the cost. City officials, however, said noise and the lack of both insurance and a site doomed the plan. Last week, the Simpson Development Co. withdrew its offer to provide the site.

"It suffers from the royal barge syndrome," said Jack L. Thompson, president of the Mid-Atlantic Helicopter Association. "People look up in the sky and say, 'Oh, there goes that fat cat.' "

In a separate matter yesterday, Lawson said she supports increasing the $12,500 annual salary of City Council members.

"In light of the fact that Montgomery and Fairfax are increasing their salaries and because Alexandria City Council members receive substantially less," Lawson said, she will recommend that the City Council vote to form a community task force to evaluate the salaries.

"I'm going broke," said Moran, who has had to curtail his job as a stockbroker because of mayoral duties. He said he would support an increase because the present salary "severely limits the quality of people you can attract to public service."

But council member Lionel Hope said that he could not support a pay raise. "When we're talking in terms of budget cuts," he said, "I don't think it's a good time."

Under city law the council cannot vote itself a pay raise, but it can raise the salaries for members taking office in 1987.

In January a Montgomery citizens committee recommended raising the current $37,347 salary for its County Council members to $48,000. And this month the Fairfax County Chamber of Commerce recommended raising that county's supervisors' salaries from $21,590 to $35,000 in 1987 and to $45,000 in 1992.

In other action yesterday, the Alexandria council unanimously agreed to sell the Old Town police department building to make way for a residential development, and to allow licensed massage therapists to practice in the city. In the 1970s the city was plagued with illicit massage parlors and the council passed a strict ordinance to crack down on them. But in yesterday's vote, the council said it recognized the therapeutic uses of massage.

The police department and city jail, at 400 N. Pitt, is scheduled to move to a new $26 million facility in December.