A stampede on a bridge outside a Hindu temple killed more than 90 people in India on Sunday, with many of the victims leaping to their deaths in the water below.

Police warned that the number could rise further as medics struggled to make their way through hordes of pilgrims to reach the scene of the tragedy -- the latest in a string of disasters at religious festivals.

While officials said the panic appeared to have been sparked by a false rumour, witnesses said that the situation escalated when police weighed in with batons.

"The death toll has risen to 91 and 10 others are in a critical condition," Deputy Police Inspector D.K. Arya told AFP after the tragedy in the Datia district of central Madhya Pradesh state.

Arya, who had earlier put the number of dead at 60, said that those in the most critical condition were being treated in Datia's Government Hospital.

Police and state government officials said the stampede at the Ratangarh temple was triggered by rumours the bridge might collapse after being struck by a heavy vehicle around lunchtime.

"There were rumours that the bridge could collapse after the tractor hit it," said Arya. "Many people are feared to have fallen into the river."

Other police sources said that some 20,000 people were on the bridge over the River Sindh when the stampede broke out.

Large crowds began converging on the site from early morning, according to witnesses, as Hindus celebrate the end of the Navaratri festival.

The festival is dedicated to the worship of the Hindu goddess Durga, which draws millions of worshippers to temples, especially in northern and central India.

Up to 400,000 devotees were already inside or around the temple in Datia district, which is about 350 kilometres (220 miles) north of the state capital Bhopal, when the stampede took place.

Witnesses said the situation was exacerbated by police charging at the crowds with heavy wooden sticks known as lathis.

"Police lathi-charge during the panic run worsened the situation, forcing many to jump off the bridge," 28-year-old Manoj Sharma, who lives in the nearby village of Bhander, told The Times of India's website.

However Arya insisted "there was no baton-charge" by the police.

Uma Shankar Gupta, the state's home minister, said authorities had not yet determined why the stampede had broken out, but downplayed suggestions that security to deal with the crowds was inadequate.

"There were safety measures in place, this is an annual event," he told reporters.

"We don't yet have information on how this happened, as our focus is on the rescue effort."

Ashok Argal, a federal lawmaker from the region, placed the blame on crowds trying to rush across the bridge.

"It is wrong to say there were any administrative lapses. The administration had taken steps and made fool-proof arrangements to avoid any untoward incident," he told AFP.

"Sometimes there is little cooperation from people and people are always in a hurry, because of which this unfortunate incident occurred."

The Times of India reported that crowds could be seen pelting police with stones as frustration grew over the rescue operation.

Efforts to reach the injured and ferry them to hospital were being hampered by the huge volume of traffic in the area.

A team of around 20 medics had however managed to reach the scene of the tragedy, and the casualty wards of nearby hospitals were being emptied to cope with the influx of victims, the newspaper added on its website.

The state's chief minister Shivraj Singh Chouhan announced payouts of 150,000 rupees ($2,500) to the families of those killed, and 50,000 rupees to the injured.

India has a long history of deadly stampedes at religious festivals, with at least 36 people trampled to death in February as pilgrims headed home from the Kumbh Mela religious festival on the banks of the river Ganges.

Some 102 Hindu devotees were killed in a stampede in January 2011 in the state of Kerala, while 224 pilgrims died in September 2008 as thousands of worshippers rushed to reach a 15th-century hill-top temple in Jodhpur.

Prime Minister Manmohan Singh was among those to express condolences over Sunday's tragedy.

"On this day of festivities, our hearts and prayers are with the victims and their families," he said in a tweet.

Narendra Modi, leader of the Hindu nationalist opposition Bharatiya Janata Party which is hoping to oust Singh's Congress government in next year's general election, said his "prayers are with the victims and their families".

The stampede comes only weeks before Madhya Pradesh is due to hold elections for the state assembly.