Accompanied by CPM leader Surya Kanta Mishra, Mr Pranab Kumar Gupta and Sudipto's sister Sumita Sengupta met the Governor to seek justice for his son.
Sudipto, a member of the CPM's student wing, was arrested while protesting with other activists against Ms Banerjee's government for delaying college elections.
Sudipto's colleagues say he was beaten mercilessly on his head.
The police says that while the students were being taken to prison, Mr Gupta fell out of a bus, hit his head on a lamp-post and died hours later in hospital. His death triggered massive protests in Kolkata.
Chief Minister Mamata Banerjee said yesterday that young activist's death was a "petty matter" and no reason for students to protest over.
Sudipto's father, anguished by Ms Banerjee's comments, today said he does not understand why such statements are being made. He said he just wants a fair and impartial inquiry.
"Have I asked for any compensation or any money... I do not need anything except a fair and impartial inquiry... any kind of statements are not going to get my child back," he said.
An autopsy report shows Sudipto had a broken jaw and fractures on his head as well as injury marks all over his body, and that all the injuries were sustained before his death.
His sister has demanded a CBI inquiry into the death of her brother.
"My father has nothing more to say, we want a CBI inquiry. The bus driver has admitted my brother was pushed off the bus and beaten. He said he was not driving fast and Sudipto did not fall off," she said.
"There are many other wounds on his body. We told everything to the Governor, we urged for a CBI probe and he heard us. Governor didn't say anything, but we are depending on him," she added.
The Kolkata Police has come out strongly contradicting the post-mortem report. The police said that the head injuries suffered by Mr Gupta indicated that he had run into a blunt, stationary object.
The State Human Rights Commission is investigating the death.