The Federal City Council, an organization representing the most influential business and professional interests in Washington, recommended yesterday that the full 100-mile Metro subway system be completed and that a regional tax be levied to pay for it.

Those and other recommendations of the Council came after its task force completed a months-long study of the Metro and its financial and institutional programs.

The call for more regional unity, the construction of a full system and the resolution of the financial difficulties that threaten Metro comes at a time when the problems are being sharply defined and publicized. None of the major regional bodies has assumed a clear leadership role in seeking solutions.

Sol M. Linowitz, former ambassador to the Organization of American States and the president of the council, clearly wanted to leave the impression yesterday that the council is willing to help fill that void, but he winced at the word "lobbying."

The council, he said, would conduct an "educational effort" on Metro's problems. The report of the council, 26 succinct pages and address the key financial and organizational problems of the public transit system here "will certainly" be forwarded to Transportation Secretary Brock Adams, Linowitz said.

Adams and other Cabinet officers are ex-officio members of the Federal City Council, Linowitz pointed out. The task force, headed by G. Duane Vieth, a partner in the prestigious law firm of Arnold and Porter, studied five specific areas of the Metro problem: the construction program, internal Metro management, marketing, land use patterns resulting from planned Metro construction and regional taxation.

In addition to suggesting that the full Metro system should be built and that a regional taxation program should be developed to finance it, the council also recommended:

A new organizational structure to finance and operate Metro should be considered. "Many of the difficult issues faced by the (Metro) board are not truly within that board's power to resolve. They depend, instead, upon decisions by a multitude of individual local jurisdictions, plus two states . . . The resulting delays and frictions unnecessarily hamper the development of sound transportation policy."

Fares for the bus and subway system should increase along with the rate of inflation. The impact of such a policy decision on the Metro operating deficit is enormous: recent projections by Peat Marwick Mitchell and Co. have found that the deficit for running the bus and subway system in 1990 will be $90 million annually if fares advance with inflation, but $301 million if they are increased at a rate only half that of inflation. Local jurisdictions are reluctant to raise fares for political considerations. In the District of Columbia, for example, the 40-cent bus fare remained for seven years.

Local governments act more aggressively to rezone areas around selected Metro stations to attract new residential and employment centers. One of the things that has befuddled local planners is that the same people who fervently support heavy rail transit, as subways are known generically, also are virulently opposed to any increase in densities in their neighborhoods.

The federal government should locate its employment centers near Metro stations and should adopt policies that encourage the use of Metro.

The federal government should commit itself to providing 80 per cent of the money needed to retire the $1 billion in revenue bonds sold to build Metro, with the localities providing the other 20 per cent.

Metro itself should spend more money selling itself, try innovative market programs and simplified fare structures and stress good customer relations.

Members of the task force who attended the council's press conference yesterday lavishly praised Metro's general manager Theodore Lutz, who has had the job just over one year.

Stephen Ailes, a partner in the prestigious law firm of Steptoe and Johnson, and who is a former Secretary of the Army and former president of the Association of American Railroads said, "we were tremendously impressed with Lutz and appalled by the management problems they have."

Members of the Metro board, Ailes noted, "rotate rapidly and are appointed as representatives rather than to see that the system operates properly." The Metro Board was organized to supervise a tight staff of managers who would oversee a construction project. The board then inherited four bankrupt bus companies and responsibility for operating public transit here.

Completion of the full subway system should be the goal, the council said, because to do so would be cheaper in the long run than the many buses required for equivalent service, and because Metro permits more compact and efficient land use and conservation of resources.

The long-term financing goal, the council said, should be for enough tax revenue to both pay the operating deficit and the bond debt service. A 1-cent general sales tax, earmarked for Metro, or a wage tax of some kind, would do that. However, the council recognized the improbability of getting Maryland, Virginia and the District of Columbia to agree immediately on such a subject and supported current efforts for lesser taxes raised by each of the three jurisdictions.

The most talked about tax is a sales tax on gasoline, which would fall far short of covering the Metro deficit and would leave the tax burden on the politically unpopular property tax.