A US investment group linked to union pension funds holding shares in Whole Foods Market have called for chief executive John Mackey to step down from his additional role as chairman.

CTW Investment Group, a branch of Change to Win, a coalition of trade unions, wants the Whole Foods board of directors to name an independent chairman “who can quickly establish credibility with regulatory authorities and shareholders”.

The rebuke to Mackey comes after the Whole Foods chief was found to have publicly criticized rival natural and organic retailer Wild Oats Markets – now a takeover target – on Internet message boards under a pseudonym.

The disclosure came to light while The Federal Trade Commission, the US competition watchdog, was preparing its case to fight the proposed merger between Whole Foods and Wild Oats. Industry watchers have suggested Mackey’s comments could threaten the deal.

The Securities and Exchange Commission, the US shares watchdog, is investigating Mackey’s comments, while Whole Foods has set up a special committee to analyse the chief executive’s actions.

CtW said Mackey’s “poor judgment” has “damaged his credibility, jeopardized the proposed Wild Oats’ acquisition and triggered a Securities and Exchange Commission investigation”.

“With Whole Foods under mounting legal and regulatory scrutiny, its share price down 37% in two years, and Mr. Mackey’s leadership in question, we do not believe the creation of a special committee alone is sufficient to restore investor and regulatory confidence in the company and its management,” CtW said.

CtW works with pension funds holding over 900,000 shares in Whole Foods.