McCormick has said it is “disappointed” with the way the board of UK rival Premier Foods, owner of Mr Kipling, is “conducting itself”.
But the US firm, known for its spice brands such as Schwartz, has said it could be willing to improve its offer for the company.
Premier this week rejected a second takeover bid, worth £496m, from McCormick, saying the offer undervalued the company.
And Premier, which also owns Bisto Gravy, yesterday announced Japanese instant noodle maker Nissin Foods has agreed to buy a 17.27 per cent stake in it from US private equity firm Warburg Pincus.
Yesterday, Standard Life Investments - which owns around seven per cent of Premier - criticised the board's handling of the McCormick bid and Nissin stake offer.
David Cumming, head of equities at Standard Life Investments, said he wanted to company to re-engage with McCormick.
He said: “We note with some dismay the timing of Nissin's acquisition of a stake in Premier Foods. In our view, this does not reflect well on the Premier Foods Board's objectivity and commitment regarding its engagement with McCormick and consequently its desire to pursue maximum value for shareholders.”
And now McCormick has responded by accusing Premier of “conducting itself in a way that denies Premier Foods' shareholders the opportunity to consider McCormick's highly attractive cash offer”.
The company said it felt the current offer, equal to 60p per share, was fair. But added: “McCormick is, however, willing to consider increasing its latest offer if justified following its confirmatory due diligence.
“McCormick believes that an all cash offer should be well received by Premier Foods' shareholders, employees, pensioners, creditors, and other stakeholders.”