It was not immediately clear how many people were on the two-lane bridge over the Sindh River in the Chambal region of Madhya Pradesh when the stampede started. Local media said some 500,000 people visited the temple and some were headed home when the rumors began.
Police wielding sticks had charged the crowd to contain the rush and people retaliated by throwing stones at the officers, D.K. Arya, deputy inspector general of police, said. One officer was badly injured.
The state has ordered a judicial inquiry.
Prime Minister Manmohan Singh expressed "deep sorrow and shock over the loss of lives" and asked local officials to help the injured and the families of the dead.
"On this day of festivities, our hearts and prayers are with the victims and their families," the prime minister's office said in a statement.