India, especially the Government of India never supported or encouraged the LTTE or any other terrorist organisation in Sri Lanka. There were individuals and organisations in Tamilnadu who were sympathetic and helpful towards the LTTE and other Tamil fighters. But that is a natural sentiment when we consider the very powerful love of the Tamil people for their language and those who speak it anywhere in the world. Tamilians, in contrast to the people of many other states in India literally worship Tamil language.
The Tamil fighters never considered themselves as Hindus, though they were mainly Hindus. They considered themselves as Tamils first and Tamils last. The Hindu nationalists in India never felt any affinity towards the Tamil fighters and any enmity towards the Buddhist extremists. The Government of India was more worried about a separate Eelam or Tamil state in Sri Lanka as it could encourage Tamils in India. If there are around three million Tamils in Sri Lanka, there are more than 60 million Tamils in India.
Tamil separatism had some support in India at the time of independence and for a few years after it. It was DMK that championed separatism in the name of Dravidanadu. They abandoned it later and now after seventy years and also after becoming partners in the Central Government in New Delhi they know how large and tempting is the honeypot in NewDelhi, when compared to the small booty available in Chennai!
It must also may be noted that it was the discriminatory attitude of the successive Sri Lankan Governments that led to the resentment of the Tamilians and the quarter century civil war. If the Government of India had favored and actively supported the LTTE the result of the civil war would have been different! The assassination of Rajiv Gandhi had turned even those groups in Tamilnadu who had sympathies towards LTTE against them. It was the greatest blunder committed by Prabhakaran that led to the destruction of his outfit and himself.