The rebels' suicide bomb campaign struck terror
Prime Minister Atal Behari Vajpayee, speaking after returning to Delhi from a trip to south-east Asia, said he had "no intention" of lifting it.
But he said India might allow the Tigers' chief negotiator, Anton Balasingham, to come to India for medical treatment on humanitarian grounds.
India's main opposition Congress Party has called for the extradition of Tamil Tiger leader Velupillai Prabhakaran.
It says Mr Prabhakaran should be brought to justice for his role in the assassination of the former Indian prime minister, Rajiv Gandhi, in 1991.
India is one of several countries to have banned the Tamil Tigers and declare it a terrorist organisation.
'Shock' over statement
In a rare news conference on Wednesday in northern Sri Lanka, Mr Prabhakaran announced an end to the suicide bombings which have struck terror over the years in Sri Lanka and India.
And he asked both India and Sri Lanka to lift their bans on his organisation.
The rebel leader described Rajiv Gandhi's assassination as a "tragic incident that happened 10 years ago".
But in a statement, the Congress Party said Mr Prabhakaran's statement had shocked all Indians.
"We cannot tolerate anybody making light of this unfortunate event," senior party leader Arjun Singh said.
"Prabhakaran was the sole architect of this tragic incident and we can never forget this," he added.
Trial demand
The party called upon the Indian Government to take all legal steps necessary to bring Mr Prabhakaran to justice.
It said that the Congress Party was not opposed to the Sri Lankan peace process which is being brokered by the Norwegian Government.
But it added that the rebel leader was a "proclaimed offender" in India's eyes and his attempt to legitimise his political status did not negate the fact that the Tamil Tigers was a terrorist organisation.
Rajiv Gandhi sent in Indian troops to keep peace in northern Sri Lanka in 1987 - a move that angered the Tamil Tigers.
His widow, Sonia, now heads the Congress and is India's opposition leader.