A train heading for the southern port city of Chittagong and one bound for Dhaka collided early on Tuesday in Brahmanbaria, about 100km east of the capital, crumpling three compartments of the southbound train.

"When I came out of the train, I saw dead bodies without heads, without legs, without hands," Mohammad Moslem, 50, who was among the passengers, many of them asleep at the time, told Reuters by telephone.

"We were so close to death, but Allah saved us," added Moslem, who was riding on the train headed for the port.

Television broadcast images of doctors treating people for broken limbs and head injuries at hospitals.

"So far, 16 bodies have been recovered," district official Hayat Ud Dowlah Khan told Reuters by telephone, warning the toll could rise during the rescue effort by fire, police, border guard and army officials.

"More than 40 injured people have been admitted in hospitals," Khan said, with some in critical condition.

Prime Minister Sheikh Hasina expressed shock and sorrow at the injuries and loss of lives, urging officials and the public to provide support for the victims.

It was not immediately clear how the two trains came to be on the same track and the government has ordered an investigation.

"One of the trains might have violated the signal, leading to the tragedy," one police official, Shayamal Kanti Das, told reporters.

Railway accidents in Bangladesh happen relatively frequently, many at unsupervised crossings, and also because of the poor condition of tracks.

Australian Associated Press