Conagra had raised its offer to $94 a share from its previous unsolicited bid of $86 a share. Its original offer for Ralcorp was $82 a share. Ralcorp has rejected all Conagra's offers.

Last month, Ralcorp decided to separate its Post-brand cereals unit from its predominantly private-label business to create two companies.

Conagra said it would continue to consider its options with respect to this potential transaction and has no further comment at this time.