The Metro board adopted a controversial plan yesterday to construct subway tunnels for a long-delayed section of the Green Line from the Fort Totten rail station in Northeast Washington to the Avondale area of Prince George's County.

The action, described as a breakthrough by District and Prince George's officials, was aimed at settling a dispute that has blocked construction of the Green Line's northeastern branch since the 1970s. Officials said the vote appeared to end the last major battle over the Green Line's route.

Earlier proposals for the section east of Fort Totten had drawn objections from neighborhood residents, the National Park Service and the Catholic Archdiocese of Washington. The dispute centered largely on plans for laying tracks above ground near South Dakota Avenue NE and in other areas.

Under the new plan, Metro officials agreed to dig subway tunnels for the route instead of building ground-level or elevated structures. Spokesmen for the park service and the archdiocese said the revised plan appeared acceptable, but some residents said the plan stops short of their demands.

The board's action was among several developments yesterday affecting the Green Line, the only unopened line the the planned 103-mile Metro system. Other developments included:

* Officials said they have reached an agreement aimed at ending another dispute over the Green Line's route through College Park. The agreement, expected to be endorsed by the College Park City Council possibly as early as next week, calls for steps to reduce noise from Metro trains in residential areas.

* The House, in a budget measure adopted yesterday, included a provision that would allot $250 million for Metro subway construction in fiscal 1986, an amount in line with the transit agency's plans for financing the Green Line's construction. The Senate has voted, however, to reduce Metro spending to $187.5 million.

* Metro officials took a key step aimed at awarding a more than $50 million contract to build the Green Line's Shaw station at Seventh and R streets NW after an extensive investigation. Officials rejected a bid by a group alleged to have engaged in "sham" minority-business practices. The action is expected to clear the way to award the contract to another bidder.

In the past year, Metro officials have settled a series of disputes that had blocked the Green Line's construction. Work has begun on the southern portion of the line with the construction of subway tunnels in Anacostia, which were delayed by a court challenge. The Metro board ended that conflict in Prince George's by choosing a southern terminus near Branch Avenue.

In April, the board voted to resolve another prolonged battle by adopting a plan to build Green Line tunnels, mainly beneath New Hampshire Avenue NW, to connect a proposed Columbia Heights station at 14th and Irving streets NW with Fort Totten.

The new plan for the section between Fort Totten and Avondale drew objections from neighborhood groups chiefly because of concern over noise and other disruption. Opponents argued that the tunnels will not be deep enough. Metro officials have disputed these contentions.

Everett W. Scott, a longtime critic of Metro's plans and a leader of the Lamond-Riggs Citizens Association, warned that a court challenge is likely. Other groups have expressed differing views.

Lucille F. Brown, president of the North Michigan Park Civic Association, said the group is "supportive of the modified plan," but has urged further steps to reduce disruption. Mozelle E. Watkins, an Advisory Neighborhood Commission chairman, said residents have sought another hearing on the issue.

In Prince George's, officials said, the revised plan will reduce disruption for Avondale residents and for the archdiocese, which owns several nearby facilities, including St. Ann's Infant and Maternity Home. Park service concerns focused on Fort Totten Park.

Metro officials said the revised plan will increase construction costs for the section by $7.6 million to a total $147.1 million.