Azam Khan said he was "stepping down on moral grounds," the BBC reported.
"Though the incident took place outside the Kumbh Mela premises, I take moral responsibility and resign as the in-charge of the Kumbh," Khan said.
The 36 dead, mostly women and children, were among about 30 million Hindu pilgrims returning home Sunday after the main bathing day in the Ganges and Yamuna rivers. Officials said at least 39 people were injured in the stampede at railway platforms.
Two others were killed and in a second crush of people on river banks, Sector 12 Magistrate Abhay Raj said.
Families of the victims would be compensated, The Times of India reported.
Patwan Kumar, India's railway minister, said the huge stampede was caused by too many people being on train platforms.
"There has been no collapse of foot-over-bridge or any railing on the station. I want to [make it] clear that stampede occurred due to people reaching in large numbers," Bansal said. "We have come to know that people turned in large numbers [resulted] in stampede. ... It was not possible to accommodate a large numbers of devotees, who had reached railway station."
The Kumbh Mela religious festival spans 55 days and occurs once every six years. The event also marks the rare Maha Kumbh Mela pilgrimage, which only takes place once every 144 years. The timing of thegatherings is determined by astrology.
Hindus believe bathing at the confluence of the two rivers will help cleanse their sins and aid their salvation.