The 72-year-old actor, who is also the recipient of the Padma Bhushan and Padma Shri, took to Twitter to express his views.
"@MamataOfficial Mamata di... I am not deserving of such recognition... Most humbled and honoured by what the Nation has given me..!!," Bachchan tweeted.
Banerjee had tweeted on Tuesday that the actor deserved Bharat Ratna.
"Amitabh Bachchan is a legend in his lifetime. Padma Vibhushan is not enough. Somebody of his stature deserves a Bharat Ratna," Banerjee had said.
The 'Shamitabh' star was chosen for this year's Padma Vibhushan, the second highest civilian award of the country, with veteran actor Dilip Kumar and seven others.