State minister Azam Khan said he was “stepping down on moral grounds”.
The victims were among about 30 million Hindu pilgrims returning home after the main bathing day at the gathering.
Earlier, India’s railway minister said the stampede had been caused by too many people being on the platforms.
At least 39 others were injured in the stampede on Sunday evening. Most of the victims were women and children.
Sunday was the most auspicious of six bathing days at the Kumbh Mela, which is billed as the world’s biggest human gathering.
The festival, which is held every 12 years, expects 100 million bathers in total across its 55 days.
The present festival is also a Maha Kumbh Mela, which comes round only once every 144 years.
Hindus believe a festival dip at Sangam – at the confluence of the Ganges, Yamuna and mythical Saraswati rivers – will cleanse sins and help bring salvation.
“Though the incident took place outside the Kumbh Mela premises, I take moral responsibility and resign as the in-charge of the Kumbh,” Azam Khan, who is also a cabinet minister in the Uttar Pradesh state government, told reporters on Monday.
Earlier, Railways Minister Pawan Kumar Bansal said the railways had made “adequate arrangements well in advance” to deal with the passenger rush during the festival. In addition to “112 routine trains, we also ran 69 special trains on Sunday”, he said.
The minister denied reports that the stampede had been caused after the railing of a pedestrian bridge leading to platform number six collapsed.
“There were too many people on the platforms. The station was overcrowded,” he said.
“Attempts are being made to decongest the railway station.”
Authorities said additional trains were being run on Monday to take people out of Allahabad.
Officials said tens of thousands of people were at the railway station at the time of the stampede.
Reports said ambulances could not get to the platform for two hours to evacuate the injured to hospital or retrieve the bodies because of the masses thronging the streets and the station.
After the stampede, Prime Minister Manmohan Singh issued a statement, saying he was “deeply shocked to learn of the unfortunate incident… in which precious lives have been lost and many pilgrims to Kumbh Mela among other people have been injured”.
“I send my heartfelt condolences to the members of the bereaved families and wish those injured a speedy recovery,” he said.
Throughout Sunday, millions of pilgrims and holy men (sadhus) belonging to various Hindu monastic orders bathed at Sangam.
Carrying pennants, bow and arrow and banners, many danced and beat drums. Some arrived on gaudily decorated chariots. Others arrived on horses. Most were dressed in saffron.
The sadhus, many of them naked, dreadlocked and smeared in ash, ran to the river amid heavy security.
More than 14,000 policemen, along with paramilitary forces and commandos, were deployed to ensure security on Sunday.
Police officers, many of them on horseback, had a hard time controlling the crowds, as many of the bathers lingered to gaze at the colorful processions of the holy men.
Kumbh Mela chief Devesh Chaturvedi said “by evening the number of bathers had crossed 30 million”.
The bathing on Sunday took place at 18 main locations along the river bank.
The Kumbh Mela has its origins in Hindu mythology.
Many believe that when gods and demons fought over a pitcher of nectar, a few drops fell in the cities of Allahabad, Nasik, Ujjain and Haridwar – the four places where the Kumbh festival has been held for centuries.
The Kumbh Mela is a mass pilgrimage in which Hindus gather in locations along the holy rivers Ganges, Yamuna and the mythical river Saraswati.
There are three different kinds of kumbh: an ardh (or half) kumbh is held every six years at two set locations; a purna (full) kumbh is held every 12 years at four set locations.
The 2013 gathering is a Maha Kumbh and that only happens after 12 purna kumbhs, every 144 years, and always at Allahabad. Astrology determines most aspects of the festival, including its exact date and length.
Kumbh Mela in numbers:
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