Federal trade Commissioner Paul Rand Dixon yesterday apologized to Arab Americans for his slur against Ralph Nader in a general statement that was not accepted by Nader and prompted calls from members of the House for Dixon's removal.

"I deeply regret a remark I made . . . which could be interpreted as a derogatory reference to Mr. Nader's ethnic background or to others of Arab descent," Dixon wrote in a letter to the National Association of Arab-Americans. "I did not intend to convey any such meaning and I apologize to all who are concerned for having made the remark in question."

During a Jan. 17 speech before th Grocery Manufacturers of America, Dixon referred to Nader as "a son of a bitch" and "a dirty Arab." Nader and his organization have in the past criticized Dixon's actions during his 16-year tenure at the Federal Trade Commission.

"His bigotry was directed specifically and it should be withdrawn specifically and I have not received a letter from him," Nader said yesterday. "The bigger issue is whether a high government official should reflect such bigotry and not be reprimanded for it by his superiors."

The White House refused comment in response to questions from reporters regarding the President's feeling about Dixon's statements. But Rep. Benjamin Rosenthal (D-N.Y.), chairman of a House subcommittee with oversight jurisdiction over the FTC, wrote a letter to Dixon and President Carter demanding Dixon's removal because "even his apology cannot dispell the cloud which has been cast over his independence and discretion in the many proceedings before his agency in which Mr. Nader participates."

Sixteen other congressmen signed the Rosenthal letter, including Rep. John Moss (D-Calif.), chairman of the oversight subcommittee of the House Commerce Committee. Rep. Edward Koch (D-N.Y.), termed Dixon's apology unacceptable and called for his impeachment by Congress.

In a House speech Koch asked if Dixon had used the terms "dirty Jew" or "dirty Christian," would "there (be) any question but that there would be an uproar?"

The director of the National Association of Arab-Americans, Michael Saba, to whome Dixon addressed his letter, said calls and telegrams to his organization indicated a desire that Dixon resign.

"We feel his response is incomplete," Saba said. "Dixon basically said he regrets the name 'could be interpreted as a derogatory reference.' There's no question in our minds it very definitely was a derogatory reference. You can't separate individuals from groups and he still has not apologized to Nader."

Fourteen consumer and public interest law advocates, including the president of Common Cause, called for Dixon's resignation on the ground he had "forfeited his usefulness as a member of a consumer agency."