Police charged three close aides of a popular actor and politician with culpable homicide and negligence on Sunday, after a stampede at his rally in southern India killed at least 40 people, officials said.

Some 27,000 people thronged a public road in Tamil Nadu state in the hope of seeing the politician, known by the single name of Vijay, on Saturday but panic broke out, triggering a deadly crush.

Police filed a case against three senior members of Vijay's party, whom they identified as Bussy Anand, GR Nirmal Kumar and VP Mathiyazhagan.

"A case has been registered and the investigation will reveal all who are involved," senior police officer S Davidson Devasirvatham told reporters.

All three have been charged with "culpable homicide not amounting to murder" and negligent conduct endangering human life.

Witnesses cited hours of delays, insufficient police presence and people falling from a tree branch onto the audience as reasons contributing to the crush.

Vijay was addressing the rally in Karur district when the crowd surged suddenly, forcing him to halt his speech.

Videos on social media showed him tossing water bottles to supporters shortly before the panic broke out.

"I am at a loss for words to express the pain my heart endures," the 51-year-old star said in a statement on Sunday.

"This is indeed an irreparable loss for us," he said, adding that he would pay two million rupees (HK$175,000) to each of the victims' families as compensation.

Nine children were among the dead. (AFP)