Strongly condemning the killing and expressing grief, Chief Minister K Palaniswami said it was 'ghastly' and promised tough legal action against the two men.
A case of murder has been registered against them and a probe was on, he said.
"I have ordered a solatium of Rs five lakh to the family of the girl," he said.
The girl, a class X student, was set ablaze in her village, Sirumadurai, about 28 km from here, allegedly by 57- year old Murugan and Kaliaperumal (53) on Sunday, a senior police official told PTI.
"She was rushed to the Government Medical College Hospital here where doctors said she sustained 80 per cent burns. She died today without responding to treatment," he said.
The girl in her dying declaration to a magistrate named the duo and made it clear they had set her ablaze, the official said.
"Based on her statement to the magistrate, we have arrested the two men."
The incident triggered an outrage, including on social media, with netizens demanding examplary punishment for the two men.
To a question, the police official said that both the accused and the family of the girl had enmity that spanned several years.
According to preliminary investigation, "the deceased and the accused men are relatives and belong to the same village. The families of the accused men and the dead girl had enmity over a couple of issues like those related to land," he said.
Adequate number of police personnel have been deployed to maintain law and order in the village which is near the temple town of Thiruvennainallur.
The girl's body was handed over to her family for burial, the official said.
DMK and its allies including the Left parties and AIADMK's ally PMK sought tough action against the culprits.
Condoling the girl's death, DMK president M K Stalin said his party will extend its support to get justice for the girl.
Only exemplary punishment will protect children and women from such crimes, he said adding the plight of the girl who suffered due to serious burns will outrage everyone with a heart.