An Indian express train ploughed into a crowd of Hindu pilgrims in the country's east Monday, killing 37 and triggering a riot that left one of the drivers dead, an official said.

The Hindu pilgrims were crossing the tracks at a station in the state of Bihar when the high-speed passenger train struck them, injuring dozens, a senior police officer said.

"The death toll is now 37," S.K. Bharadwaj, an additional director general of police, who is overseeing security at the crash site, told AFP.

"Dozens of people have been injured. We do not have exact figures of those injured because they were taken away to various hospitals," he said.

Angry crowds went on the rampage, converging on the Rajya Rani Express which stopped after the accident, attacking its drivers and leaving one dead with another seriously injured, Bharadwaj said.

"One of the drivers of the train who was beaten up by the agitators has died. The other driver is struggling for his life in the hospital," he said.

The crowds also set carriages on fire and ransacked the station in the small town of Dhamara Ghat, some 248 kilometres (154 miles) from the state capital Patna, local railway chief Arun Malik told AFP.

"Six carriages have been set on fire and the station has been ransacked by the mob. Our staff have fled the station fearing attacks," Malik said.

Prime Minister Manmohan Singh appealed for calm "so that the relief and rescue operations can be carried out without any hindrance."

"The Prime Minister has expressed deep sorrow and shock at the loss of lives of pilgrims caused by the accident," the statement from Singh's office also said.

A senior railways official said it appeared the pilgrims were not aware of the incoming express train on the middle of the station's three tracks.

"Two trains were already stationary on other tracks and the Rajya Rani Express was given permission to pass," Arunendra Kumar, chairman of the national railway board, told reporters in New Delhi.

"The accident occurred because some people left the platform of the station and came on the tracks," Kumar said.

Large numbers of pilgrims had been gathering at a nearby temple to offer prayers, according to the Press Trust of India. Some of the pilgrims are Kanwarias who are devoted to Lord Shiva, the god of destruction.

There are hundreds of accidents on the railways annually.

In 2012, a government report said that almost 15,000 people were killed every year crossing India's rail which it described as an annual "massacre" due to poor safety standards.

Pedestrians guilty of "unlawful trespassing" walk across the tracks at many unofficial crossing points, the report said, adding that about 6,000 of the deaths occur in the congested and frenetic city of Mumbai alone.

Attempts to stop people riding on the roofs of trains have largely failed, vehicles routinely drive around barriers at crossings and passengers are often seen hanging out of open doors in the carriages.

The data is not broken down, but a vast majority of these deaths are people falling from the open doors of carriages or being hit on the tracks, which are mostly unsecured.

One of India's worst rail accidents was in 1981 when a train plunged into a river also in Bihar, killing an estimated 800 people.