BEVERLY HILLS, Calif. (AP) _ The director of the FBI came to Hollywood on Wednesday, and told television producers that chronicles of the FBI's last decade would make great TV.

In a speech to several hundred TV executives, FBI Director William Sessions asked the medium to continue its largely favorable depiction of the FBI and tantalized the luncheon crowd with an account of an FBI investigation.

Sessions enthusiastically recounted the FBI's successful investigation of the Chicago gang El Rukns, sprinkling his account with colorful images of an omnipotent FBI.

Encouraging the producers to make more FBI-oriented programs, Sessions said, ''Our investigations of the last 10 years, I believe, are more intriguing and have more intriguing facets than ever before.''

Sessions specifically thanked the makers of NBC's ''Unsolved Mysteries'' and the Fox Broadcasting Corp.'s ''America's Most Wanted,'' which feature current law enforcement investigations and fugitives at large.

Sessions said both programs ''help to demonstrate the depth of the responsibility that the FBI ... goes through. I would say the portrayal (on these shows) gives a sense to the American public of the difficulties we face in trying to bring these people back.''

The FBI director told the members of the Academy of Television Arts and Sciences that TV's depiction of the agency has been crucial to public awareness.

''FBI stories are very much a part of television history,'' he said. ''I would like to think that future FBI chronicles on television might reflect current issues ... and crime problems that the FBI faces in the closing years of the 20th century.''

One of the most successful TV series was ''The F.B.I.,'' broadcast by ABC from 1965 to 1974. The show starred Efrem Zimbalist Jr. as the masterful Inspector Lewis Erskine. Its stories presumably were based on real cases, and its portrayal of the FBI was always glowing.

Former FBI Director J. Edgar Hoover gave ''The F.B.I.'' full cooperation and opened FBI headquarters for occasional filming of background scenes. Many ''F.B.I.'' segments concluded with requests for information on the FBI's most-wanted list, including a 1968 appeal for Martin Luther King assassin James Earl Ray.

''The F.B.I.'' was updated by ABC in 1981, but ''Today's F.B.I.,'' starring Mike Connors, lasted less than a year. The sequel also had the approval of the FBI, which gave the show's makers real FBI files.

This fall, NBC will debut a new drama called ''Mancuso, FBI,'' based on the courageous FBI agent seen in the network's miniseries ''Favorite Son.''

Mancuso, played by Robert Loggia, was portrayed as a toss-out-the-book maverick, marking time for his retirement, when politically motivated FBI bosses gave him an impossible assignment because they were sure he would fail.

The FBI had no consulting role in the miniseries, and if the character stays true to form in the weekly series - still in the development stage - the FBI can be expected to reject any involvement.