The announcement of the bounty by the BJP Yuva Morcha leader on a video created nationwide furore, with politicians cutting across party lines demanding stringent action against Mr Varshney. The BJP also distanced itself from the controversy by disowning its leader.
The youth wing leader had earlier said that he was deeply hurt at a lathicharge on Tuesday on a crowd at Birbhum, about 180 kilometres from Kolkata, when they had had gathered to celebrate Hanuman Jayanti.
Calling Ms Banerjee a "demon", the BJP youth wing leader said, "When I saw the video, I only had one thought... that if anyone gets me Mamata Banerjee's head I will give them 11 lakh."
Mr Varshney has since apologised for his statement and withdrawn the bounty announced in the morning.
He told reporters that he made this announcement in a fit of rage and emotional outburst after seeing video footage of the lathicharge in West Bengal.
Meanwhile, former legislator of the Samajwadi Party Jameer Ullah also jumped into the raging controversy on Wednesday evening and sought to get the tongue of the BJP Yuva Morcha leader chopped off.