Meeting just five blocks from the White House, directors of the Metropolitan Washington Council of Governments--who represent all the local governments of the capital region--voted yesterday to endorse a freeze on the development of nuclear weapons that is strongly opposed by President Reagan.

The 12-to-3 vote by the board, with two abstentions, was an unusual and perhaps unprecedented action for the 25-year-old organization, which traditionally has limited itself to regional issues.

There was little debate yesterday, since the directors had discussed the resolution at length in July when it was proposed by Mayor Sammie A. Abbott of Takoma Park. That city's council and the governing bodies of several other area jurisdictions already have taken similar actions.

The resolution advocates that the United States and the Soviet Union freeze the development, testing and deployment of nuclear weapons.

Abbott was pleased. "The Soviet population is just as averse to a nuclear war as we are," he said.

The opposing votes were cast by mayors John Freeland of Rockville and John Russell of Fairfax City and by Arlington County Board member Walter B. Frankland. Abstaining were City Council members Margaret Inman of Alexandria and Robert Hubbell of Falls Church.