Thirteen people were killed and 31 seriously injured as the private bus in which they were travelling collided with a truck on the Agra-Lucknow Expressway in Firozabad district of Uttar Pradesh, a senior police official said on Thursday.

Senior Superintendent of Police Sachindra Patel said the accident happened around 10 pm on Wednesday in Nagla Khangar police station area.

The sleeper bus was going from Delhi to Motihari in Bihar when it hit the container truck from behind.

The injured, some of whom are in a critical condition, have been sent to a Saifai hospital in Etawah for treatment.

Prime Minister Narendra Modi condoled the death of people in the accident and hoped for fast recovery of those injured.

"The road accident on the Agra-Lucknow Expressway in Uttar Pradesh has caused deep grief. Many passengers have lost their lives ... My condolences to the families of the victims in this hour of grief. I wish those injured recover soon," the Prime Minister's Office said in a tweet quoting Modi.

Uttar Pradesh Chief Minister Yogi Adityanath has directed the district magistrate and other senior officials to reach the accident site and oversee the relief work.

He also issued directives for proper treatment of the injured, a statement issued by the state government said.