In a memo he sent to a colleague at the Justice Department, William P. Cook said he agreed to become the senior lawyer at the Immigration and Naturalization Service last year in hopes that he could turn INS Commissioner Gene McNary "and the INS away from the historical tendency toward self-destruction that grips this agency."

But now that three Cook memos have been leaked to congressional committees and newspapers, some Justice Department officials privately indicate that they think the INS general counsel may be the one who self-destructed.

In the memos, Cook described McNary as "a press release politician," said the commissioner believed Attorney General Dick Thornburgh was "mortally wounded" and would soon be leaving, that the Justice Department was "a mess" and that McNary's reorganization of the INS was "a disaster."

"Gene is convinced that he has control of the service because he has centralized control of the budget and personnel hiring," said one Cook memo. "Since he has not removed any of the incompetents who worked here at headquarters for {former commissioners Alan C.} Nelson and {James} Buck, the inmates are once again running the asylum."

One official familiar with the memos said they so infuriated McNary that he threatened to strip Cook, who is paid $74,400 a year, of his duties supervising the agency's 355 lawyers and a $33 million budget. The memos began circulating last week at the same time that a draft General Accounting Office report sharply criticizing the INS management became public.

The Cook memos and the GAO report reinforce the INS's image as an administrative quagmire and illustrate how divided senior INS managers are over the agency's goals and direction. "The management team he {McNary} has brought in is more adept at fighting with each other than fighting illegal immigration," Cook said.

When McNary is "out of town, the power grab is on, and I include myself in this," Cook said. One official who Cook said had been cut out of the agency's operations was deputy commissioner Ricardo Inzunza, who "was put into satisfy the Hispanic community demand that they get someone high in Justice."

A spokesman for the INS declined to comment on the memos and referred calls to the Justice Department. Rex J. Ford, an associate deputy attorney general, said in a statement that the department is concerned about "the long-standing problems at the INS" and said a newly created management team will "rectify these problem areas."

"While we will heed any constructive criticism, we do not find gossip about internal bickering within the INS either useful or relevant to the process," Ford said.

John H. Trattner, a former State Department spokesman and author of "A Survivors' Guide for Government Executives," said Cook appears to have violated a basic rule for public officials.

"I would never put that down on paper. I would save it for personal conversations with my friends," he said. "If you feel strongly about a situation, you should confront the individuals or organization."

Cook, 38, a former senior attorney in the Justice Department's Office of Legislative Affairs, was reported to be in Arizona and did not return telephone calls.

In the memos, he acknowledged that his relationship with McNary had "continued to deteriorate" and suggested he might have to leave the agency.

Arthur C. Helton, director of refugees' rights for the Lawyers Committee for Human Rights and a frequent INS critic, said he fears the memos will wound "the new leadership" at the agency.

"I count both Gene McNary and Bill Cook among the new leadership that has made progress on . . . humanitarian issues," he said. Unlike some Reagan administration officials at the INS, the two have been willing to listen to advocacy groups and have frequently taken advice "from outside the agency," Helton said. That may have proved troubling to career INS employees "who would like to hold the new leadership hostage," Helton said.

Helton was one of those Cook criticized in his memos. Helton "is one of the most litigious attorneys we litigate against and at any one time has many suits pending against INS and the department," Cook said.

Stephen H. Legomsky, a law professor at Washington University in St. Louis and another of the commissioner's outside advisers, said in a letter to Thornburgh last week that "the INS is a massive, sprawling bureaucracy that no human being could single-handedly overhaul in a year" and that McNary deserves credit for "the rapid progress of the past year."

Cook is described in his biography as "one of the drafters of President Bush's government-wide Ethics Act of 1988 as well as many immigration-related pieces of legislation." A 1978 graduate of the Southwestern University Law School in Los Angeles, he joined the Justice Department in 1984 after a four-year tour in the Navy.