Former Gov. Bill Waller, whose 1972-76 administration was marked by racial harmony and business and trade development, announced yesterday he will seek to unseat Sen. James O. Eastland in the June 6 Democratic primary.

"Don't we need a 60-hour-a-week man in Washington rather a six-hour-a-week man?" Waller asked at a campaign luncheon attended by about 350 supporters. "I think that one full-time, aggressive U.S. senator can do a lot to get Mississippi off the bottom. Let's end the crisis in Washington. Let's send a new man to work on the problems."

The 51-year-old Jackson attorney, who won the governship with Eastland's support, indirectly characterized Eastland as "isolated," and complained. "It seems you have to be a gib shot in Mississippi to talk to a senator."

Waller becomes the third, but most potent candidate to announce against Eastland. The 73-year-old Eastland, president pro tem of the Senate and chairman of the Judiciary Committee, has said he will seek a seventh consecutive six-year team.

Eastland in recent weeks has moved to squelch criticism of his past racial attitudes and his age by bringing blacks and young people into his campaign, attracting many whose first active exposure to government came in the Waller administration.

Dr. Robert L. Robinson, who was appointed by Waller to head the state's industry-seeking Agricultural and Industrial Board, and Henry J. Kirksey, a black-activist involved in legislative reapportionment battles, have also announced as Democratic candidates.

Democratic Gov. Cliff Finch, meanwhile, has called a meeting of supporters for April 6, the night before the qualifying deadline, but declined to explain why. He has announced he will accompany a state trade mission to the Mideast and Africa the last week in April and first week in May and his intentions are unclear.

The chairman of the Mississippi Republican party, state Sen. Charles Pickering of Laurel, is expected to announce in the next few days his intention to run in the November election.