The Trinamool, on the other hand, said the chant was being used to "spread terror" and alleged that by resorting to the slogan, the saffron party was "tarnishing" Lord Ram's name.
"It is strange that someone is reacting against some chant. If anyone says 'Ma, Maati, Maanush' (Trinamool's slogan) in front of me, will I lose my cool? By using undesirable words on hearing the slogan, Trinamool is destroying Bengal's culture," Roy said.
Banerjee on Thursday lost her cool for the second time and chased a group of youth shouting 'Jai Shri Ram' in front of her convoy enroute Naihati in the North 24 Parganas district.
Referring to Banerjee's speeches during the recent Lok Sabha poll campaign, Roy said it was not Bengal's culture to utter something like "will slap the Prime Minister" or "will make the Prime Minister do sit-ups".
"I have mentioned earlier that there is some sort of an imbalance in her state of mind," Roy said.
Countering BJP's allegations that the Trinamool members have a problem with "Jai Shri Ram" chants, West Bengal Urban Development Minister and Kolkata Mayor Firhad Hakim said: "There is nothing wrong in 'Jai Shri Ram' but if people resort to spreading terror by chanting it, it becomes a crime."
Elaborating further, Hakim said there is "no problem in saying Allah Hu Akbar" but when terrorists kill innocent people and utter "Allah Hu Akbar", it becomes a crime.
The people of Bengal are used to "Jai Ma Kali" and "Jai Baba Taraknath" chants, but the BJP workers' behaviour is not in sync with Bengal's culture, he said.
"They (BJP) are tarnishing the name of Lord Ram by chanting 'Jai Shri Ram' this way. His name is uttered in temples and it is pronounced with devotion. The way hooligans standing on roads are shouting Lord Ram's name to showcase their strength is utterly disgraceful," Hakim said.
Even those who believe in Hindutva are protesting against it, Hakim added.
Meanwhile, BJP MP from Barackpore Arjun Singh on Sunday announced that he will send 10 lakh postcards to Banerjee with "Jai Shri Ram" written on them.
In a counter, state Food and Supplies Minister Jyotipriyo Mullick said that he is planning to send 20 lakh postcards to Prime Minister Narendra Modi and Union Home Minister Amit Shah with "Jai Hind" and "Jai Bangla" written on them.
( With inputs from IANS )