Peltz, whose fund is P&G's fifth-largest shareholder, has been locked in a prolonged battle with the maker of Gillette razors and Tide detergents and has been pushing for a seat on the company's board.
Yacktman said it owned $1.3 billion (970.44 million pounds) worth of P&G shares and cited Peltz's sizeable stake in P&G and his experience with other consumer products companies for its support.
"Current outside board members have no meaningful economic investment in the company's success or failure," Yacktman said in a letter to P&G's board on Thursday.
P&G, in response to Yacktman's letter, said the company "did not ask for this proxy contest" and is committed to preventing anything from derailing the progress it is making in terms of its strategy and financial results.
P&G has argued that Peltz's plan to boost shareholder value by organizing the company into three largely autonomous business units would result in higher costs, lower profits and another restructuring that could lead to a breakup of the company.
"One voice on a board cannot upend a successful strategy," Yacktman said in a letter to the company's board, referring to P&G's argument that Peltz could derail the progress it has made.
P&G's shareholders will vote on Oct. 10 on whether to add Peltz to the board.
Trian is the second activist fund in five years to target the consumer goods company.
In 2012, Pershing Square Capital Management invested in P&G and called for the ouster of its then chief executive, Robert McDonald. McDonald was replaced a year later, and in May 2014 Pershing exited the position.
Trian was not immediately available for comment.
P&G's shares, which have risen 6.5 percent since Peltz announced his stake in the company in February, were flat at $93.55 in afternoon trading.
(Reporting by Gayathree Ganesan and Sruthi Ramakrishnan in Bengaluru; Editing by Anil D'Silva and Maju Samuel)