The Republican-dominated National Labor Relations Board has significantly weakened power of the agency's general counsel by requiring that he submit all legal briefs to board attorneys.

The action will place higher responsibility on the NLRB staff attorney, solicitor Hugh L. Reilly, who formerly worked as an attorney for the National Right-to-Work Committee. The switch was viewed by some as an attempt to give the NLRB a more conservative cast.

At a meeting last Wednesday, the board voted 4 to 1 to weaken the control of general counsel William A. Lubbers, a Carter administration appointee, over the litigation unit, which handles all appeals of NLRB decisions and enforces board decisions in the courts if necessary. The decision was conveyed to agency employes Thursday, but not given to the public until Friday.

Don A. Zimmerman, a political independent appointed by President Carter, was the only member to vote against the change. President Reagan's three appointees and Howard Jenkins Jr., a Republican reappointed by Carter, supported it.

Lubbers, whose four-year statutory term expires next April, declined comment.

Reilly served as executive assistant to new board chairman Donald L. Dotson, when Dotson was assistant secretary of labor for labor-management relations. Dotson brought Reilly with him when he became board chairman this year.

The AFL-CIO initially opposed Dotson's nomination because of his hiring of Reilly, but backed off by the time the nomination came before the Senate.

Last night Dotson denied an earlier report that Lubbers had been stripped of his authority, saying the unit will remain under Lubbers but all actions must be reviewed and approved by Reilly.

Agency sources said the board took the action, in part, because it was afraid the litigation staff might not accurately reflect its views before the federal courts. While the NLRB makes decisions in labor disputes and organizing battles, it must rely on the federal courts to enforce the decisions. Past board members, under both Republican and Democratic administrations, have sometimes complained that the agency's litigation staff substituted its legal determinations for the board's when presenting cases in court.

Reilly referred all questions to Iliff McMahan, an agency spokesman, who minimized the concerns of some members of the litigation staff. He said the change was made simply to improve coordination between the board and the legal staff.

A spokesman for Rep. William L. Clay (D-Mo.), chairman of the House subcommittee on labor-management relations, said Clay was "quite concerned" about the action because it raises a "number of legal and political questions" and "it looks like a blatant political move."

The general counsel is required to undergo Senate confirmation, while the board's solicitor is not.