The chairman of a House Judiciary subcommittee has asked the Equal Employment Opportunity Commission to review its decision to yield to White House and Justice Department pressure and shelve a court brief in support of quotas and affirmative action.

In addition, the chairman of the full Judiciary Committee, Rep. Peter W. Rodino Jr. (D-N.J.), has asked the EEOC to give Congress all correspondence with the Reagan administration--including the briefs the commission had prepared but voted not to file last week at the request of presidential aide Edwin Meese III and Attorney General William French Smith.

"As subcommittee chairman I am very concerned about executive branch pressure...which has resulted in the Equal Employment Opportunity Commission's withdrawal from participation in Williams vs. City of New Orleans," Rep. Don Edwards (D-Calif.) wrote to the commission last week. "This is especially disturbing since...your March 21st correspondence to Justice states that adoption of its position would significantly impact on the existing and future remedies in cases to which EEOC is a party.

"I would encourage the commission to reevalutate its decision to withdraw in light of its obligation as lead agency on equal employment opportunities," Edwards wrote.

After a meeting that included EEOC Chairman Clarence Thomas, Meese and Smith at the White House, the EEOC voted last week to rescind an earlier unanimous vote to enter the New Orleans case. In that case, a quota system has been established for promotions so that more blacks would be brought into supervisory positions.

The Reagan administration has repeatedly opposed quotas, but administration officials said they consider the issue not a policy decision but "a jurisdictional decision made by the Department of Justice." The administration argues that, as an agency of the executive branch, the EEOC is subordinate to the president's representative, the Justice Department.

"This case has clarified our standing," commission chairman Thomas said yesterday. "It points out to Congress the chink in our armor. We were created to take the lead responsibility in setting civil rights policy in court but we are in the executive branch which has its own opinions. So there is a contradiction there that has to be ironed out....this commission should be independent and this case clearly shows why."

But Eleanor Holmes Norton, head of the commission in the Carter administration, disputed Thomas on the EEOC's standing. "The commission has been bullied," she said. "Congress gave the commission the authority to file briefs at all levels below the Supreme Court..."

At the NAACP Legal Defense and Education Fund, which is party to the case, director Jack Greenberg said, "The administration is opposed to traditional civil rights laws and now it is silencing the EEOC."