He was 74.
Dave was unanimously selected as BJP's Rajya Sabha member for two successive terms (1990-2002).
He was also appointed as the chairman of Narmada Jal Sichai Nigam, a state government unit, by Chief Minister Narendra Modi.
"Sad to hear about demise of party colleague Anantbhai Dave, who played a key role in the development of Kutch. May his soul rest in peace," Modi tweeted.
BJP national vice-president Purushottam Rupala and state unit president R C Faldu also expressed grief at the death of the leader.