WASHINGTON (AP) _ The Reagan administration's No. 2 budget official, Joseph R. Wright Jr., denied to Congress on Monday that he acted improperly when he called an Energy Department regulator about a multimillion-dollar case against an oil company run by his father.

''This case was fixed, whether Mr. Wright intended that to occur or not,'' said Sen. Albert Gore, D-Tenn. ''Mr. Wright could be telling the truth and we could still have a damning case against him - a very serious lapse in judgment that was unethical.''

Wright, the deputy director of the Office of Management and Budget, is also chairman of the President's Council on Integrity and Efficiency.

His father runs Anchor Gasoline Corp. of Tulsa, Okla., and its subsidiary, Canal Refining, of Church Point, La. Overall, the family controls 20 percent of the stock, with the younger Wright owning 3 percent, valued at about $250,000.

Anchor is the target of a long-delayed Energy Department complaint which seeks to recover $16 million in alleged overcharges and interest. A similar case against Canal Refining seeks $23 million. The overcharges allegedly occurred in the 1973-81 period when the government controlled prices on oil and petroleum products. Reagan lifted those controls almost immediately after he took office.

The younger Wright acknowledged to the Senate Governmental Affairs Committee that on Sept. 23, 1982, nine days after charges were first brought against Anchor, he called Rayburn Hanzlik, head of the Economic Regulatory Administration at the Energy Department, and asked him to meet with company representatives.

Wright said his father had told him earlier ''he was having trouble with what he considered bureaucratic delays and foot-dragging in getting a decision from the Department of Energy on a matter involving pricing regulation. He thought there should be somebody in Washington, D.C., his people could talk to. He did not then, nor has he since, discussed the nature or details of the matter with me.''

Wright said he emphasized in his call to Hanzlik: ''One, all I was asking for was a meeting - nothing else. Two, the company I was referring to was a family company, and, three, I neither wanted nor expected any special treatment.''

''Well, what was he supposed to think?'' asked Gore. ''He (Hanzlik) was the head of the enforcement division, which was then involved in a bitter dispute with the OMB over how much money it was going to get'' in Reagan's budget.

Hanzlik, in an interview with The Wall Street Journal, said that ''a 120- second phone call is not what I would consider a fix,'' but conceded ''there's an appearance problem ... it was not good judgment'' for Wright to have called him.

Hanzlik also said that he told Wright ''You can have the people (from Anchor) come in here to find people who are more reasonable.''

Gore and Sen. Thomas F. Eagleton, D-Mo., noted for the record that Hanzlik did meet with Anchor representatives, and the case was subsequently ordered transferred from the Kansas City office of the Energy Department to the Dallas office, which recalculated the figures and concluded that Anchor owed no penalties.

''You say that what you and your dad wanted was express justice,'' said Eagleton. ''What you got was a slow train ... that saved $39 million. That's big bucks.''

Eagleton said he had talked to three Energy Department officials who told him it was their understanding the case was to receive special handling because a high administration official was involved with Anchor.

The case was revived early this year after one of Hanzlik's aides was questioned about it by the Energy Department's inspector general. The Dallas office, on Washington's order's, reviewed the figures again and, this time, arrived at the same recommendation as had the Kansas City office.

Sen. William V. Roth, R-Del., repeatedly asked Wright if he had discussed the case in detail with his father or anyone else. ''No sir,'' said Wright. ''I first got a feeling for the amounts of money involved when I walked with a reporter a month ago. I was flabbergasted.''

Roth: ''Do you think you created the appearance of impropriety?''

Wright: ''I do not.''

Roth: ''And if you had to do it all over again?''

Wright: ''I would not. I have no desire of appearing a week or two in the press, or appearing before this committee, although I do enjoy this committee.''