The lives were lost at the main railway station where 10 corpses wrapped in white sheets could be seen on a train platform several hours after the incident which occurred in the early evening, an AFP photographer said.
Dozens more were injured in the crush and some local television channels put the death toll as high as 20.
Local officials said that the railings on a bridge at Allahabad station had given way under the pressure of the mass of people, while eyewitnesses told local media that the police had baton-charged the crowd leading to panic.
“People were taking rest on these railings and the railings could not take the load. The joints broke,” a spokesman for the local Uttar Pradesh state, Ashok Sharma, told AFP.
The tragedy came at the end of a day which organisers had earlier declared a success after a record number had taken a bath in the holy waters of the Ganges, which is said to cleanse pilgrims of their sins.
“By afternoon over two crore (20 million) people had taken the holy dip and by evening the numbers crossed three crore (30 million),” top local official Devesh Chaturvedi told a press conference.
Police had been stretched in controlling the vast crowds, he admitted, and one person had died for unknown reasons, while another later succumbed to injuries sustained in a crush.
Thousands of volunteers on duty and police urged pilgrims to take one short bath and then leave the waters to make space for the flow of humanity behind them which stretched for kilometres (miles).
The Kumbh Mela, which began last month and ends in March, takes place every 12 years in the northern city of Allahabad. Smaller, similar events are held every three years in other locations around India.
This year’s Mela is big even by previous standards, with astrologers saying a planetary alignment seen once every 147 years made it particularly auspicious for some pilgrims.
“This is a rare combination of planets which would bring in good times for some zodiac signs and adverse effects for others,” said Amarpal Sharma, a local astrologer.
The bathing takes place at an area called Sangam, the confluence of the rivers Ganges and Yamuna and a third mythical waterway called the Saraswati.
Devotees believe entering the water cleanses them of sin and frees them from the cycle of rebirth.