The Metropolitan Washington Council of Governments typically concerns itself with zoning, transportation and other items of local concern. Yesterday, the 17 representatives of area governments found themselves grappling with nuclear arms control and after a lengthy debate, they decided to head back to familiar territory.

"We have gone beyond our level of official competence," said Nancy K. Falck, Dranesville's voice on the Fairfax Board of Supervisors. "We are beyond the well-recognized actions of local government."

The council debated a proposal sponsored by Takoma Park which would ask President Reagan for an immediate freeze on the production of nuclear weapons. Voters in the Maryland suburb were among the first nationwide to support the idea.

A grass-roots effort to end the buildup of nuclear arms has spread from New England towns across the country, gaining the endorsement of several local and county governments in Maryland and Virginia. The District has put the question on the ballot for this fall's elections.

Supporters crammed into COG's downtown meeting yesterday, but the council's representatives said they were uncomfortable in trying to determine where area citizens stand on nuclear weapons.

Gaithersburg Mayor Bruce A. Goldensohn said, "We were not elected as representatives for this kind of issue."

The mayor of Rockville, whose city council has a nuclear freeze resolution under consideration, denounced the issue. The movement, said Mayor John R. Freeland, is based on "a buzzword, and I don't think most people know what it means." He refused to support it.

The COG representatives voted 9 to 8 to table the proposal. They also postponed a decision on public hearings designed to evaluate the area's civil defense evacuation efforts.

Sammie A. Abbott, Takoma Park's 74-year-old, civic-activist mayor who sponsored the nuclear freeze proposal, left cursing the representatives as they moved on to discuss local pollution and traffic problems.

"The ironic thing is," he said, "the biggest water pollution, the biggest pothole is going to come from a big, goddamn blast!"