The councillor, Neeraj Gupta, has been caught on camera slapping a junior engineer of Delhi's civic body after an argument. He is seen trying to hit him again, but is restrained by people.
Mr Gupta is a councilor from Sangam Vihar, a densely populated area home to mainly low income families.
"There is no space of violence in democracy. As a principle no one, especially a public representative, should resort to violence," said BJP spokesperson Nalin Kohli.
"What does the BJP want? If they think they can win this election through violence, they are mistaken," said Aam Aadmi Party's Sanjay Singh.