At least 24 people were killed and more than 40 others injured when a speeding private bus packed with passengers plunged into a dry river bed after breaking through railings of a bridge in Madhya Pradesh's Khargone district on Tuesday morning, Agriculture Minister Kamal Patel said.

As many as 41 passengers were injured in the accident and undergoing treatment in various hospitals at Khargone and Indore, Patel, who is also minister in-charge of the district, told reporters.

Patel said Khargone district's Assistant Regional Transport Officer (ARTO) was suspended after it came to light that the ill-fated bus was overloaded and speeding at the time of the accident.

There were around 70 passengers in the bus which had capacity to accommodate only 37 people, the minister said.

Patel said the police have been directed to launch a drive against speeding and overloading in buses in the district.

Officials said 18 seriously injured persons were referred to Indore for further treatment, while 23 were admitted at the Khargone district hospital.

A magisterial probe has been ordered into the accident which took place at around 8.40 am, state Home Minister Narottam Mishra Mishra told reporters earlier.

After the bus fell off the bridge, some villagers rushed to the spot and pulled out trapped passengers from windows and rear side of the vehicle, as per eyewitnesses.

Locals were seen carrying people and offering water to the harried passengers amid hot weather, they said.

Prime Minister Narendra Modi condoled the loss of lives in the road crash and announced an ex-gratia of Rs 2 lakh each for the next of kin of the deceased.

The bus broke through railings of the Dasanga bridge and fell into dry bed of the Borad river near Dongargaon village, Mishra said.

Earlier in the day, the officials said the vehicle was carrying around 50 passengers.

Madhya Pradesh Chief Minister Shivraj Singh Chouhan separately announced an ex-gratia of Rs 4 lakh each to the kin of those killed in the tragedy.

The seriously injured persons will be given Rs 50,000 and the passengers with minor injuries will get Rs 25,000 each, Mishra said.

The state government will bear the cost of treatment of the injured passengers, he added.

Prime Minister Modi expressed grief over the loss of lives and wished speedy recovery to the injured passengers.

"The road accident in Khargone is very saddening. My condolences to those who have lost their loved ones in this accident. Also, I wish speedy recovery to all the injured. Under the supervision of the state government, the local administration is providing all possible help on the spot," Modi was quoted as saying in a tweet by the Prime Minister's Office (PMO).

"An ex-gratia of Rs. 2 lakh from PMNRF (Prime Minister's National Relief Fund) would be given to the next of kin of each deceased in the bus accident in Khargone, Madhya Pradesh. The injured would be given Rs 50,000," he said.

Khargone Collector Shivraj Singh Verma, Superintendent of Police Dharamvir Singh and local MLA Ravi Joshi were among those who visited the accident spot.

Former Union minister and Congress leader Arun Yadav, who hails from Khargone, also expressed grief over the tragedy.

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