Three key private sector unions in the Metropolitan Washington Council, AFL-CIO, have cut back their dues to the central labor group in a dispute over public sector unions dominating the council's executive board and endorsements in the District's current political races.

The reduction in dues payments cuts the council's operating income by about 15 percent and takes away a major funding source for its political activities just as it is trying to start a voter registration drive and reestablish itself as a power base in city politics.

The council endorsed a losing candidate in the 1978 mayoral election, Walter Washington, and spent $25,000 on a get-out-the-vote effort on Washington's behalf.

In addition, the three unions reducing their support for the council--the Hotel and Restaurant Workers, Local 25; United Food and Commercial Workers, Local 400, and the International Union of Operating Engineers, Local 99--are shifting their contributions to the political action arm of their own umbrella group, the Food and Allied Services Trade Council.

The food council has already decided to endorse its own slate of candidates for mayor and City Council seats. The food union has given those candidates maximum campaign contributions and has begun voter education work on their behalf.

The hotel workers union will begin this month to cut its monthly contribution to the metropolitan council from about $1,200 to less than $200. The operating engineers are reducing their monthly contributions from $280 to $20, and the food and commercial workers are reducing dues payments from $1,275 to $75.15.

Joslyn Williams, president of the metropolitan council, said the council is a democratic organization with decisions made by votes of the membership that make it impossible for either the private or public sector unions to control the group. He said the reductions in contributions would not cripple the group.

"The reduction in dues only diminishes their influence in the labor community," Williams said. "The labor council as a whole is bigger than any one organization . . . . Any one of them can choose to pull out or cut back but they are damaging themselves more than anything else.

"You've got to remember," he added, "that membership is voluntary. The United Auto Workers pulled out of the AFL-CIO and the AFL-CIO survived."

Earlier this month the metropolitan council failed to endorse a candidate for mayor when public and private sector unions split their vote almost evenly in an angry fight. The public sector unions backed incumbent Marion Barry, and the private sector unions supported lawyer Patricia Roberts Harris.

Ron Richardson, secretary-treasurer of the Hotel and Restaurant Workers, said he and other private sector union representatives were upset at the absence of an endorsement for mayor after they had offered compromises to the public unions to enable the council to support a candidate.

Richardson said private sector groups were further angered when endorsements for the City Council ward races were delayed by the executive board of the labor council, which is dominated by officials of public sector unions.

"We have no intention of dropping out of the council," said Richardson, "but the other public sector unions are paying contributions on only 10 or 20 percent of their membership while we are paying close to 80 percent and they are running the show. Whoever is paying the piper should be calling the tune."

William Lucy, secretary-treasurer of the American Federation of State County and Municipal Employees, said the private unions' decision is not based on politics but on resentment toward Williams because he was elected president of the group on a slate of public sector union officials that defeated a private sector slate earlier this year.

"The private sector unions have dominated that council since before water," said Lucy. "Now that the public sector unions are getting together their issues and candidates, they're saying they don't want to play and they are going to do their political action through the food council . . . It's got to hurt the labor council; it reduces the cash flow."

Ken Reichard, vice president of the United Food and Commercial Workers, said he did not think the reduction in dues payments is a warning to labor officials in the council that the labor movement is in trouble.

"I think this will make most people realize there are serious problems," Reichard said, "and say 'Quit the fighting and let's get things together instead of working against each other on all this petty stuff.' "

Richardson, secretary-treasurer of the food council, said that group has about 45,000 dues-paying members, about half of the dues-paying members claimed by the metropolitan council.

The food council has endorsed and given contributions to Harris; City Council member David A. Clarke, who is running for City Council chairman; candidate Ruth Dixon in Ward 3; candidate Douglas E. Moore in Ward 5, and John E. Warren, a school board member running for the City Council seat in Ward 6.

The metropolitan council was scheduled to make similar endorsements when it voted on an endorsement for mayor but the executive board asked that those votes be put off. A coalition of public and private sector unions behind Clarke for City Council chairman obtained an endorsement for Clarke that night, but the others have been delayed until after July 7, the deadline for candidates in the Sept. 14 primary to file petitions for office.