Chief Minister MK Stalin said eight children and 16 women were among the 36 people who died in the district of Karur in Tamil Nadu during a political rally by Tamilaga Vettri Kazhagam, Vijay's party.
Earlier, state MP Senthil Balaji told reporters that 58 people were hospitalised.
Vijay, one of Tamil cinema's most popular actors for three decades, has drawn massive crowds to his public meetings since launching his political party in 2024, which has targeted both the state ruling party DMK and the Prime Minister Narendra Modi's Bharatiya Janata Party.
He is campaigning ahead of state elections that are to be held in early 2026.
Videos from local media show thousands of people surrounding a large campaign vehicle on top of which Vijay is seen standing and speaking.
During the rally, visuals showed Vijay throwing water bottles from the top of the vehicle to fainting supporters and calling for police help when the crowd became uncontrollable.
"My heart is broken; I am in unbearable, indescribable pain and sorrow," Vijay wrote on X.
"I express my deepest sympathies and condolences to the families of my dear brothers and sisters who lost their lives in Karur. I pray for a speedy recovery for those who are undergoing treatment in the hospital."
At least 44 doctors from the nearby districts of Tiruchirappalli and Salem were sent to Karur, media reports said.
Stalin has announced 1 million Indian rupees ($A17,200) each to the families of the victims who died in the incident and set up an inquiry panel.
This is not the first time Vijay's rallies have faced safety concerns.
At least six deaths were reported by media following the first meeting of his political party when it was launched in October last year.
Despite police-imposed restrictions, including limits on convoy size and venue changes, the sheer scale of public turnout has repeatedly overwhelmed local infrastructure.
"The unfortunate incident during a political rally in Karur, Tamil Nadu, is deeply saddening," the prime minister said in a post on X.
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Large crowds had gathered for the meeting, part of Vijay's ongoing state tour for his political party Tamilaga Vettri Kazhagam.
Vijay, who is a well-known actor and goes by only one name, launched a political party last year and began campaigning this month ahead of state elections that are to be held early next year.
State MP Senthil Balaji told reporters that 58 people were hospitalised after what he said was a stampede.
He added that Tamil Nadu Chief Minister MK Stalin will visit the area on Sunday.
"The unfortunate incident during a political rally in Karur, Tamil Nadu, is deeply saddening," Prime Minister Narendra Modi said in a post on X.
Calls to Tamil Nadu state's health ministry and Tamil Nadu Chief Minister MK Stalin's office went unanswered.
"The news coming from Karur is worrying," Stalin said in an X post, adding that he had directed ministers and officials to provide urgent medical aid to those who collapsed at the Karur rally and ordered additional assistance from nearby Tiruchirappalli.
At least 44 doctors from the nearby districts of Tiruchirappalli and Salem were sent to Karur, media reports said.
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