This time around, Procter & Gamble is fighting Mr. Peltz’s attempt to get a seat, saying he is a late arrival to a corporate turnaround that is already underway.

Mr. Peltz, who owns a $3.5 billion stake in Procter & Gamble, has said he is not looking to oust any board members or the chief executive, David Taylor. If he wins a seat, he hopes to convince the other directors, including Kenneth Chenault, the chief executive of American Express, and Meg Whitman, the chief executive of Hewlett-Packard Enterprise, that the company should be organized from its current multilevel “matrix” structure to three clear global business units to improve accountability. He also contends that a study should be conducted to understand why Procter & Gamble’s once-vaunted innovation machine appears to have stalled.

“This is different from the normal activist slate, which is seeking to replace much of the board or the C.E.O.,’’ said Charles M. Elson, director of the John L. Weinberg Center for Corporate Governance at the University of Delaware. “Here, he’s simply seeking input into the board process. He seeks a change of direction and I think he’s right. I think the company has stalled.”

In the last decade, Procter & Gamble’s total return — stock performance plus reinvested dividends — was around 77 percent. That is about half the returns for peers like Kimberly-Clark and Colgate-Palmolive.

Procter & Gamble argues that Mr. Peltz is not providing any new ideas. The company’s management, including its board and Mr. Taylor, a longtime Procter & Gamble veteran who was named chief executive nearly two years ago, has already identified the changes that need to be made and is in the midst of making them, it argues.

Furthermore, the company says its plan is yielding results, noting that it has delivered total shareholder return of 28 percent since Mr. Taylor took over, outperforming its peers.