At least 31 people have been killed and dozens of others injured when two passenger trains derailed and plunged into a river in the central Indian state of Madhya Pradesh at the same spot simultaneously.

At least 300 people have been rescued so far as frantic emergency efforts are under way.

The Kamayani Express from Mumbai bound for the Hindu holy city of Varanasi derailed near Kudawa train station and went tumbling into river at about midnight.

A second train, the Mumbai-Jabalpur Janata Express, which was running from the opposite direction also derailed when it crossed the bridge on the swollen Machak river.

The bridge, located between two stations, was reportedly damaged owing to the recent heavy rains. Machak river is about 160kms from Bhopal, the capital of Madhya Pradesh.

"Seven bogies of Kamayani Exress and engine plus three coaches of Janata Express derailed between Khirkiya and Bhirangi stations near Harda," said Indian Railways spokesperson Piyush Mathur.

The army has been drafted in to lead the rescue measures. Local personnel and villagers are also assisting the emergency workers in the operation.

Another spokesperson for the railways department Anil Saxena said there was "water on tracks and the bridge was submerged. So the last bogies of Kamayani Express got derailed. Simultaneously, on the other track the engines and coaches of the Janata Express also got derailed".

India's Railway Minister Suresh Prabhu has ordered an inquiry into the incident and announced compensation for the victims.

Prime Minister Narendra Modi tweeted: "My prayers with the injured. Authorities are doing everything possible on the ground. The situation is being monitored very closely."

"The two train accidents in Madhya Pradesh are deeply distressing. Deeply pained over the loss of lives. Condolences to families of deceased."

Train accidents are not uncommon in India primarily due to poor maintenance and the absence of necessary safety measures.

India has one of the largest railway networks in the world and trains remain a key mode of transportation for millions of Indians every day.