An NAACP leadership rift widened yesterday with quarreling about how soon the organization's board should meet to discuss the sudden suspension of Executive Director Benjamin L. Hooks and whether it should curb the power of Chairman Margaret Bush Wilson.

The organization announced Friday that Wilson had suspended Hooks without prior board consent.

Five key members of the 64-person board, some contending that the reputation and effectiveness of the nation's oldest civil rights organization are at stake, last week called for a board meeting next Saturday morning at the NAACP national headquarters in Brooklyn. They proposed discussing Hooks' suspension and Wilson's powers.

Yesterday, however, Wilson, working through acting Executive Director Thomas I. Atkins, said that the call for a Saturday meeting was improper. Atkins instructed board members to disregard that notice and to meet instead June 11 in a hotel outside Chicago.

The sole stated purpose of that meeting, he said, would be discussion of and appropriate action on the suspension.

Several who had sought the earlier meeting said they would meet this Saturday anyway. "That means nothing to me, brother," NAACP national Vice Chairman Kelly M. Alexander Sr. of Charlotte, N.C., said yesterday, referring to the June 11 date.

"The majority of the board members are going to meet Saturday. I'll be there . . . . I am interested in the NAACP, and I am going to see that nobody is going to destroy it," Alexander said.

"There will be a meeting" this Saturday, said Hazel Dukes, chairman of the 77-chapter New York State NAACP, whose board voted unanimously last Saturday to ask that Hooks' suspension be rescinded. She said her board has since directed her to call for Wilson's resignation.

Wilson, an attorney in St. Louis, could not be reached for comment yesterday. A reporter who phoned her law office was told that she was out of town. Atkins also was unavailable for comment.

Hooks, 58, a Baptist minister and former member of the Federal Communications Commission, was relieved of his duties last Wednesday. His three-year contract ends in October. In its formal announcement of the suspension Friday, the NAACP did not elaborate.

Sources inside the organization said, however, that the action climaxed a lengthy feud between Wilson, board chairman since 1975, and Hooks, executive director since 1976, over management, direction and control of the organization. The NAACP, whose membership exceeds 150,000, has an annual budget of about $7 million.

Wilson had been critical of Hooks' stewardship, saying the organization had a poor reputation in the philanthropic community, was not fully serving its members and no longer had an activist posture. She had sought an investigation of NAACP operations with a view toward hiring someone other than Hooks to handle day-to-day operations.

Some sources said they viewed that criticism as part of an effort by Wilson to run the organization herself. They said she intervened in some daily administrative matters, did not inform Hooks of management decisions she made and often ordered him to prepare voluminous reports for board meetings, then gave him only limited time to present them.

Alexander, president of the North Carolina NAACP since 1948, said the suspension tarnished the organization's image and stymied its operations.

"This situation is so serious and we're getting so many calls from all over the United States about this matter that it is imperative that we meet as soon as possible to resolve this issue," he said.

"People want the board of directors to dispense with this issue so the orderly management of the NAACP can continue without delay," he said.

The feud comes as the NAACP prepares for its 74th annual convention July 11-15 in New Orleans. All announced presidential candidates and a top Reagan administration representative are to be invited.