Police in India registered a criminal case against leaders of Tamil actor Vijay's political party after a stampede at his rally killed 39 people, a senior police official said on Sunday.

The dead included children and more than 50 people were injured in Saturday's stampede in the southern state of Tamil Nadu, where Vijay was campaigning for his Tamilaga Vettri Kazhagam party ahead of state elections early next year.

Tamil Nadu police filed the case, the first step toward potential charges, "against TVK party senior leaders Bussy Anand, Nirmal Kumar and V.P. Mathiyalagan, and the investigation is under way," senior police official V. Selvaraj told Reuters.

"TVK originally sought permission for a gathering of 10,000 people, but the actual crowd was more than double," he said.

Vijay, one of Tamil cinema's most bankable actors for three decades, has drawn massive crowds since launching his party last year. He said he was "heartbroken" by the stampede in the Karur district, pledging support for the victims' families.

Tamil Nadu Chief Minister M.K. Stalin announced compensation of 1 million rupees ($11,300) per family.

The state has appointed a commission led by a retired judge to investigate the cause of the stampede.

Prime Minister Narendra Modi posted on X that the incident was "deeply saddening".

During the rally, footage from local media showed thousands of people surrounding a large campaign vehicle on top of which Vijay was speaking. He was seen throwing water bottles to fainting supporters and calling for police help when the crowd became uncontrollable.

Vijay's TVK has targeted the state's ruling party, DMK, and Modi's Hindu nationalist Bharatiya Janata Party.