The Justice Department's probe of the Rev. Martin Luther King Jr.'s murder has proveded fresh insighs into the department's biggest continuing problem - keeping the FBI under the control of the Attorney General.

"A report by a special department task fence, made public Friday, concluded that the FBI was not implicated in the April 1, 1968, shooting of King in Memphis.

Instead, the report said, the bureau's investigation of the murder was thorough and left virtually no grounds for doubting that James Earl Ray, now serving a 99-year sentence for the murder, was the sole assassin.

In other respects though, the report is harshly critical of the FBI's behavior in the King case and the failure of the Justice Department, which is responsible for supervising the bureau, to correct its excesses.

The report says, in effect, that under three successive Attorneys General - Robert F. Kennedy, Nicholas deB. Katzenbach and Ramsey Clark - the FBI functioned like an unguided missile subject only to the whims of its longtime director, the late J. E gar Hoover.

During the King murder investigation, for example, the report says that Hoover and other FBI officials treated Clark, who was then Attorney General, "with a significant degree of disdain," frequently bypassing him and failing to keep him informed of its actions.

The task force also retraced in considerable detail the campaign of vilification, wiretapping and illegal breakins waged by the FBI from 1963 until King's death in an effort to discredit him as the principal leader of the civil rights movement.

This campaign, the report makes clear, was rooted in Hoover's animosity toward King and was made possible because Justice Department officials were fearful of intervening or were so lax in their supervision that the FBI was able to do things behind their back.

Much of this information already had been made public through press and congressional disclosures following Hoover's death in 1973. As a result, Edward H. Levi, the Attorney General during the past two years, was forced to devote the bulk of his efforts to reasserting Justice Department control over the bureau.

He imposed strict guidelines on the FBI for the conduct of domestic security investigations, and forced the bureau's current director, Clarence M. Kelley, to acknowledge the Justice Department's authroity over FBI activities. However, the bureau's critics have continued to voice doubts about whether Levi's changes were sufficient to prevent future FBI efforts to operate in its old free-wheeling and unsupervised manner.

The degree to which it did so in the 1960s is underscored by the task force's description of FBI conduct during the King murder case. At almost every turn, the report notes, FBI personnel displayed "marked discourtesy" to Clark and his aides at the Justice Department.

Early in the investigation, gor example, when Clark announced plans for making a progress report to the nation, Hoover advised his subordinates in a memo: "We are not going to make any progress reports."

Shortly afterward, when the FBI identified a suspect known as "Galt" (later learned to be Ray's alias), it filed a criminal complaint agaist him in Birmingham without consulting the Justice Department. The report quotes FBI files as saying the complaint was filed in Birmingham rather than Memphis because the bureau "could not rely on the U.S. attorney at Memphis" to give it a free hand.

When Clark complained to an assistant FBI director about being "kept in the dark," the official summarily "hung up the phone." After Ray's capture in England, when Assistant Attorney General Fred Vinson was sent to London to arrange for extradition, the FBI told its attache there to be "diplomatic but firm with Vinson and under no circumstances should Vinson be allowed to push our personnel around."

In summarizing these incidents, the report said, "The task force views this lack of coordination and cooperation as highly improper." But it also adds, in an obvious criticism of Clark:

"In fairness to the bureau, it has to be observed that it is the obligation of the Justice Department to insist on its prerogatives. We do not think it effectively did so in the King murder case."

Regarding to Hoover-inspired harassment campaign against King, the task force said the FBI had arguable legitimate reasons for initiating an investigation because of evidence that one of King's key advisers allegedly had Communist ties.

When Hoover presented this evidence to Attorney General Kennedy in 1963, the report says, Kennedy was "sincerely concerned . . . since proposed civil rights legislation was then very vulnerable to the attack that Communists were influencing the direction of the civil rights movement."

The report says Kennedy was sufficiently alarmed to take the initiative in suggesting that the FBI begin wiretapping surveillance of King. He subsequently changed his mind for a time, but in October, 1963, Kennedy finally bowed to Hoover's persistent pressure and authorized the bugging of King's residence of office.

This electronic surveillance continued under Katzenbach and Clark, and much of the intelligence gathered, some of it dealing with King's sex life, was widely disseminated among government officials. During Kennedy's time in office, the report adds, "without his knowledge," the FBI broadened its activities to include illegal harassment tactics, and these continued under Kennedu's successors.

Yet, the report concludes, the investigation of King quickly established that he was not under Communist influence and should have been ended shortly after it was started in 1963. That it was allowed to continue for more than five years prompted the task force to make this observation:

"The continuing security investigation reflects that the Attorney General and the (Justice Department) division charged with responsibility for internal security matters failed badly in what should have been firm supervision of the FBI's activities."