The holy bathing began on Saturday afternoon and peaked after midnight, festival official Satish Kumar Sharma said.
More than 12,000 police officers were guarding the nearly 20-square-kilometer (7.7-square-mile) site, India's government said.
Indian Prime Minister Manmohan Singh said he was "deeply shocked" by the deaths and promised to extend "all possible help" to state authorities.
"I send my heartfelt condolences to the members of the bereaved families and wish those injured a speedy recovery," Singh said in a statement issued by his office. He pledged that those injured and the families of those killed would receive compensation.

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