James C. Miller III, director of the Office of Management and Budget, has found that conduct by his deputy, Joseph C. Wright Jr., had created "the appearance of conflict of interest" in the public mind but has assured Wright that he should remain in his post.

In letters made public yesterday by the OMB, Miller said "the matter is closed" and Wright vowed not to repeat an "error in judgment" that had prompted two congressional inquiries and one by the Federal Bureau of Investigation.

At issue was the ethics of a telephone call Wright made to a Department of Energy official in 1982 to set up a meeting for officers of Anchor Gasoline Corp. of Tulsa, Okla., to discuss a $16 million government fine against Anchor for overcharging. Wright had a $250,000 stock interest in Anchor, which was then headed by his father. The claim has not been settled.

Miller said in his letter that he does not think that Wright violated the section of OMB's ethical code that forbids government officials to represent a party other than the United States in a government proceeding. Earlier, the Department of Justice had stated that Wright had not violated this provision.

Possible conflict with the second part of the code, which requires officials to avoid the appearance of impropriety, was "very much more troublesome," Miller said. While there was evidence that Wright sought to avoid the appearance of conflict of interest, Miller added, Wright's telephone call "ended up causing a furor," even though there is no evidence that it "influenced the outcome of the legal matter."

Miller found, however, that his deputy had already been "disciplined severely by this episode." He praised Wright's work and assured him: "You retain my every confidence." He directed Wright to reaffirm his intention to avoid any future appearance of conflict of interest and to clear with the budget office's general counsel any discussions with officials "even remotely related" to his or his family's financial interests. Miller Hits Aide's Action OMB Deputy Called DOE About Oil Firm Los Angeles Times

James C. Miller III, director of the Office of Management and Budget, has found that conduct by his deputy, Joseph C. Wright Jr., had created "the appearance of conflict of interest" in the public mind but has assured Wright that he should remain in his post.

In letters made public yesterday by the OMB, Miller said "the matter is closed" and Wright vowed not to repeat an "error in judgment" that had prompted two congressional inquiries and one by the Federal Bureau of Investigation.

At issue was the ethics of a telephone call Wright made to a Department of Energy official in 1982 to set up a meeting for officers of Anchor Gasoline Corp. of Tulsa, Okla., to discuss a $16 million government fine against Anchor for overcharging. Wright had a $250,000 stock interest in Anchor, which was then headed by his father. The claim has not been settled.

Miller said in his letter that he does not think that Wright violated the section of OMB's ethical code that forbids government officials to represent a party other than the United States in a government proceeding. Earlier, the Department of Justice had stated that Wright had not violated this provision.

Possible conflict with the second part of the code, which requires officials to avoid the appearance of impropriety, was "very much more troublesome," Miller said. While there was evidence that Wright sought to avoid the appearance of conflict of interest, Miller added, Wright's telephone call "ended up causing a furor," even though there is no evidence that it "influenced the outcome of the legal matter."

Miller found, however, that his deputy had already been "disciplined severely by this episode." He praised Wright's work and assured him: "You retain my every confidence." He directed Wright to reaffirm his intention to avoid any future appearance of conflict of interest and to clear with the budget office's general counsel any discussions with officials "even remotely related" to his or his family's financial interests.