NEW YORK — Procter & Gamble is hitting back at activist investor Nelson Peltz, saying in a letter Tuesday that he’s not entitled to a board seat just because he wants it.

Peltz’s hedge fund has a 1.5 percent stake in the consumer products company. He has used that position to push for a seat on the board to help reverse what he says is P&G’s disappointing financial performance over the last decade.

In its letter, P&G urged shareholders to vote against Peltz, saying he has offered no new actionable ideas for the company.

“‘Why not?’ appears to be the extent of Mr. Peltz’s reason for board membership,” P&G wrote in a letter signed by CEO David Taylor. “This is simply not a sufficient standard. Joining P&G’s board is not an entitlement.”

Trian Fund Management, Peltz’s hedge fund, declined to comment Tuesday. Trian sent its own letter to shareholders on Monday urging them to elect Peltz to the board.

The Cincinnati-based company’s annual meeting is slated for Oct. 10.

P&G, whose brands include Tide detergent and Crest toothpaste, said it is working on restructuring its business and cutting costs.

Shares of Procter & Gamble Co. rose 39 cents to $91.22 in afternoon trading Tuesday.