DuPont said adding a Trian principal was "not in the best interests of all DuPont shareholders," but it was open to having a dialogue with Trian.

DuPont on Friday rejected Trian's proposal to add two nominees each to its board and the board of a unit the company plans to spin off.

The company has said it is prepared to accept one of the fund's nominees, John Myers, in an attempt to end the proxy war.

Trian, which owns a 2.7 percent stake in DuPont, said it was "open to discussing a realistic settlement", in a letter to the company's board on Monday. (http://1.usa.gov/1wPXi3H)

The fund said it had received "positive feedback" from DuPont shareholders regarding all of its nominees.

The activist investor is asking DuPont shareholders to elect a "Trian principal" and three other nominees. The fund has also identified chief investment officer Edward Garden as a "Trian principal", or an alternative to Nelson Peltz.

"It is unfortunate you have decided not to settle this proxy contest and instead have decided to use stockholders' money to continue a time-consuming, disruptive, and costly campaign against Trian," the hedge fund said. (http://1.usa.gov/1wPXi3H)

DuPont shares fell about 2.5 percent on the New York Stock Exchange, after BofA Merrill Lynch downgraded the stock to "underperform" from "buy".

The stock was trading at $78.48 on Monday morning.

(Reporting by Swetha Gopinath in Bengaluru; Editing by Savio D'Souza and Don Sebastian)