DuPont has fired another verbal salvo at activist shareholder Nelson Peltz.

In a letter to shareholders, the US chemical giant countered Peltz's criticism of its performance, noting that the company's share price has risen 18 % over the past 12 months, compared with a 7 % increase for Dow Chemical and a 14% rise in the S&P 500.

Peltz's investment vehicle Trian, which owns a 2.68 % stake in DuPont, in the past has repeatedly called for a break-up of the company to improve shareholder value.

In the shareholder letter dated Feb. 17, DuPont said it had met with Trian more than 20 times in an effort to "work constructively" with the fund. But, CEO Ellen Kullman added, the fund had nevertheless "presented an ultimatum" to management to either break up or appoint its representatives to the board of directors.

Peltz is seeking to have himself and three other nominees of his choice named to the DuPont board and has called the proxy vote a "referendum on the company's financial performance."

In early February, DuPont thumbed its nose at the investor, appointing two of its own nominees as directors. Citing "people briefed on the matter," the newspaper New York Times said one of the new directors is James Gallogly, who recently stepped down as CEO of LyondellBasell.

Dow, which is being pursued by Third Point, the hedge fund owned by activist investor Daniel Loeb, sidestepped a proxy fight with that fund in November 2014 by agreeing to add four independent directors to its board.

A proxy fight for control over DuPont, should it take place, would be fought at the annual shareholders' meeting-for which no date has yet been set.