Amid private White House concern that he may be hurting President Reagan with his sharp attacks on other black leaders, U.S. Civil Rights Commission Chairman Clarence M. Pendleton said yesterday he plans to cool his rhetoric and get "out of the way" of the "burgeoning debate" on quotas, busing, affirmative action and the administration's civil rights record.

When the debate ends "in three or four years," Pendleton added, he will favor eliminating the commission and having the Justice Department and Equal Employment Opportunity Commission monitor civil rights.

Last week Pendleton renewed his feud with civil rights leaders by saying some were behaving like "new racists."

His critics responded that he is a Reagan "lackey."

The exchange raised White House concern that the administration's leading spokesman for civil rights may be adding to strains between Reagan and blacks.

"You can go too far, and he may have now," said a White House aide. "When you are in a fight you don't want to hurt yourself. That's what we've got to watch for."

Another administration official said, "The reaction here has been totally negative. He has become the issue."

But all sides agreed that Pendleton has not been pressured to quiet down.

"I do think now it's important for me to get aside and see what the American public is talking about," Pendleton said in an interview yesterday.

"I've raised the debate to the level it is. To continue the way I've been going is, at this point, a little counterproductive . . . . Calling me names because of what I said is not a debate," he said.

"I'm getting out of the way. People know where I stand. There's no need to continue to do this sort of thing making critical comments about black leaders . I don't want to be the center of attention and be called Step'nfetchit and a lackey. I want the issues to be the center of attention. The commission has done a service by saying, 'Here is the new debate,' " he said.

Pendleton added that he would support eliminating the commission after the public has fully debated the "central issue of preferential treatment" in civil rights laws.

Civil rights activists, sharply differing with Pendleton, have argued that the debate over preferential treatment -- such as quotas and affirmative action -- is a smoke screen to divide the civil rights community while the administration retreats on civil rights programs and enforcement and on social programs to aid minorities.

Pendleton denied that he has been pressured by administration officials to halt his vocal attacks. In the past week, however, he has been the subject of mostly critical press comment and news columns.

Administration officials have complained privately that his rhetoric may be beginning to hurt the president.

But White House aides stressed that Pendleton remains "very, very popular" with Reagan. They mentioned that Pendleton's wife sat next to the president at the recent White House state dinner for King Fahd of Saudi Arabia.

Pendleton said yesterday the only criticism he has heard is from blacks. He called himself more a victim of "intra-racial racism than inter-racial racism."

He noted that Rep. Parren Mitchell (D-Md.) has called him a "lackey" for the administration and that his colleague on the civil rights commission, Frances Guest, a black Reagan appointee, has called him a "bigot."

Other blacks, he said, have called him a "Step'nfetchit" -- a reference to a fawning black character in early movies -- because of his support for Reagan policies.

"I guess I'm in good company," he joked, "because some congressman called Pierce a Step'nfetchit, too," he joked, referring to Housing and Urban Development Secretary Samuel R. Pierce Jr.

Despite the urging of some critics, Pendleton said, the administration has not asked him to resign. "Ronald Reagan could say, 'Pendleton, you're causing me too much grief and its time to get you out of Dodge City,' " he said. "What would that do for the blacks who say he should fire me?

"I'm not carrying water for the administration," he added. "I'm carrying water for myself and for the rank-and-file people, black and white, who write and call me. I don't agree with the president on everything, but we are ideologically compatible."

Pendleton said he does not regret his remarks. He felt required, he said, to do "something unique" to spur debate about civil rights issues.

Pendleton added that his life has been a study in civil rights: "I've been the first black, the only black, the integrated black, segregated black, been married to a black woman, a white woman, I've been discriminated against. I know what I'm talking about."