Political rivals, including Congress and the Samajwadi Party, attacked Mr Modi's statement as "insensitive and reflective of his mindset" over the death of Muslims in 2002 post-Godhra riots.
The BJP, meanwhile, defended the Gujarat Chief Minister's remarks, saying he has been "misinterpreted completely" and "a controversy has been created where it does not exist".
"I appeal to all to read the interview in full and not to speak out of context. It is risky," BJP spokesperson Nirmala Sitharaman said.
On the controversy around the "puppy" remarks, she said that Mr Modi meant that anybody would feel sad even if a human being came under a car.
"Clearly, this is done with an intention to appease a particular section. It is part of Congress' vote bank politics. It is part of Congress' strategy before elections," Ms Sitharaman said.
Talking exclusively to news agency Reuters today about what had happened in 2002, Mr Modi used an analogy that has in the few hours since the interview was published, become a huge controversy. Mr Modi said, "If we are driving a car, we are a driver, and someone else is driving a car and we're sitting behind, even then if a puppy (kutte ka bachcha) comes under the wheel, will it be painful or not? Of course it is. If I'm a chief minister or not, I'm a human being. If something bad happens anywhere, it is natural to be sad." (Read: Modi's 'puppy' analogy sparks political storm)