The White House and Justice Department, attempting to squelch a major internal dispute over civil rights policy, have pressured the Equal Employment Opportunities Commission successfully to withdraw an appeals court brief that sharply criticized administration stands on racial quotas and affirmative action.

The "friend of the court" brief had attacked the Justice Department's position objecting to the use of quotas in a New Orleans police department discrimination case. The EEOC said justice's position had no legal merit and was a threat to efforts to eradicate employment discrimination.

The commission unanimously approved filing of the brief in January, telling the Justice Department that the expression of conflicting views would be of "considerable public benefit."

Concerned that the administration speak with "one voice," however, top officials began a campaign to kill the brief. The campaign included a high-level White House meeting last week with presidential counselor Edwin Meese III, warnings from the Justice Department that the commission lacked legal authority to express independent views in such cases and a reminder from Civil Rights Division chief W. Bradford Reynolds that opposition to racial hiring and promotion quotas was "explicitly set forth in the Republican Party platform."

The commission voted 4 to 1 Tuesday not to submit the brief. The dissenter was the sole member not appointed by President Reagan, Armando Rodriguez.

The commission announced the reversal yesterday in a terse statement. It "would be within the public interest not to file" views that conflict with the Justice Department, the statement said. At the same time, it urged the department to "consider" the EEOC's position when writing its own brief in the New Orleans case, which is now before the 5th Circuit Court of Appeals.

In a letter sent Tuesday to Attorney General William French Smith, EEOC Chairman Clarence Thomas said the commission "strongly urges" the Justice Department to reconsider its position in light of the EEOC's objections.

"Should the Department of Justice decide not to change its position substantially," Thomas wrote, "the department's brief should indicate the difference between its position and that of the commission."

However, several sources said that during the White House meeting with Thomas, Meese said he did not favor changing the Justice Department's position and Smith said it would damage the department's brief to include mention of a contrary position that would have no legal standing.

The controversy is the latest in a series of internal skirmishes over civil rights that have embarrassed the administration. The most notable predecessor was a dispute last year over granting tax-exempt status to private schools that practice racial discrimination.

This case now in question stems from a discrimination suit by black police officers represented by the NAACP Legal Defense Fund and settled in 1981 with a broad agreement for affirmative action in hiring and promotions.

Under the agreement, the police department will promote one black to a supervisory position for every white promoted until the upper ranks are at least 50 percent black. (Before implementation of the quota system began in December, 1982, only seven of 283 police supervisors were black in a 55 percent black city.) White and Hispanic police officers are challenging the quota system.

Though similar quotas have been imposed without being overruled by federal courts, the Civil Rights Division of the Justice Department intervened in January, arguing that the quotas are unconstitutionally broad because they reward blacks who may never have been victims of discrimination and hurt innocent non-minorities.

The EEOC brief, obtained by The Washington Post, said that "nothing in the language" of the country's employment discrimination law (Title VII of the Civil Rights Act of 1964) supported the administration's position in the New Orleans case and that "no court" had ever agreed with it.

"The result of endorsing the department's contentions would be to prohibit the availability of any prospective race-conscious 'affirmative action' or employment goals," the EEOC brief said. Contrary to the administration's arguments, it added, the constitution demands "no such result."

In a March 21 letter to Smith, the EEOC wrote:

"If the Civil Rights Division's position was to become law it might well invalidate innumerable conciliatory agreements, consent decrees and adjudicated decrees to which the commission is party . . . . Even in cases where a long-continued and egregious pattern of discrimination has been proven or shown to be probable, the position would prohibit the courts from responding . . . . "

Participants in the White House meeting that led to EEOC's decision not to file included Meese; White House Counsel Fred F. Fielding; Melvin L. Bradley, a special assistant to the president who works with black groups; Attorney General Smith; Deputy Attorney General Edward C. Schmults; Civil Rights Division Chief Reynolds; Thomas, and EEOC general counsel David Slate.

"We certainly let them the EEOC know how we felt on the subject," said Justice Department spokesman Art Brill. "It never came down to directing them one way or the other. The attorney general advised the EEOC that the government should speak with one voice and that the brief we already filed was fully in line with the administration's position."

Thomas said in an interview that he and other commissioners were strongly influenced by the argument that the EEOC had no legal authority to speak independently in cases involving discrimination in the public sector. The EEOC has been speaking independently for years. And though the commission believes it does have authority, Thomas said members did not want to test it in this case especially since the commission's legal counsel partially supported that argument.

Rodriguez, the dissenter, said in an interview he felt that the commission should stick with a position it believed in, regardless of the Justice Department's objections. "The push of the Justice Department has been extremely strong and aggressive, beyond what I consider its role to be."

The combat over the New Orleans case between the EEOC and the Department of Justice began in January, when the department failed to inform the commission in advance of its intervention.

According to correspondence obtained by The Post, the full commission protested in a letter to Smith, saying the failure to consult was "a sharp departure from acceptable standards of inter-agency protocol" and a breach of the EEOC's legal designation as "the chief interpreter" of the laws against employment discrimination.

In another letter, Thomas put the administration on notice that a friend-of-the-court brief would be filed because of the "dramatic departure" from established policy the Justice Department's position represented.