He promised that parties besides the LTTE would be allowed to operate in the north-east.
The Tigers have recently apologised to Muslims, whom the LTTE expelled from Jaffna in 1990.
Later Premadasa himself initiated dialogue with the LTTE which went on for more than a year.
The separatist Tamil Tigers, or LTTE, are a proscribed terrorist organisation in many capitals.
But most pundits consider that the LTTE has, by its grisly standards, been somewhat restrained.
Before joining the political mainstream, Karuna had created the TMVP as a breakaway faction of the LTTE.
After a series of unsuccessful frontal attacks on the pass in early April, the LTTE switched tactics.
The same crushing majority also keep telling us: please do not allow the LTTE to come back.
The LTTE subsequently deployed Thayalan in Vavuniya and ordered him to continue studying until they found him a target.
Three students already being held are said to be suspects in a petrol-bombing and in putting up pro-LTTE posters.
BBC: Sri Lanka arrests: Jaffna police detain 'terror' suspects
If the LTTE is to pull out at any stage it will have to come up with another reason.
The only Tamil group now fighting the Sri Lankan armed forces is the Liberation Tigers of Tamil Eelam (LTTE).
It says the LTTE's failure to understand the changing tactics of the security forces eventually led to their defeat.
The government has ruled out allowing what remnants, if any, exist of the LTTE to return to the political mainstream.
So there is little discussion yet of just what powers will be given to an LTTE-dominated provisional administration for the north-east.
The Liberation Tigers of Tamil Eelam (LTTE) emerged under the leadership of Velupillai Prabhakaran as a ruthless and highly effective fighting force.
Still, despite the LTTE's past efforts to kill off moderate Tamils, the Tamil community is not lacking in political parties or leaders.
Kumaratunga has said she would offer the constitutional changes to the LTTE in order to open fresh negotiations to end the war.
This prompted the LTTE to launch an assault on Jaffna, whose population of some 350, 000 civilians is guarded by a 30, 000-strong security force.
Repelled by the Tigers' terrorism, and with little sympathy for Tamil grievances, most Sinhalese support the government in its campaign to obliterate the LTTE.
Sri Lanka continues to experience strong economic growth, driven by large-scale reconstruction and development projects following the end of the 26-year conflict with the LTTE.
We hope that a democratic LTTE will go back to Jaffna along with the rest of the Tamil leadership and participate in the democratic process.
The Tigers - or Liberation Tigers of Tamil Eelam (LTTE) - are fighting for a separatist state in the north and east of the island.
Meanwhile, the LTTE will seek to rebuild its financing network abroad.
Most of the fighting took place in the Tamil-dominated north, but the Tamil Tigers, or LTTE, also carried out suicide bombings in Colombo in the 1990s.
But this month it will visit the Sinhalese-majority town of Anuradhapura, where 27 people were killed and 94 injured by an LTTE suicide bomber in 2008.
When we were having discussions with the LTTE, I exchanged 44 letters with Prabhakaran, the first time he ever wrote to any politician in the south.
Her best friend, of the same age, and really called Kanchana, was killed after the LTTE gave her a gun and sent her to the front.
Anton Balasingham, its chief negotiator in Thailand, said more plainly than any top LTTE official has, so far, that it would settle for something short of independence.
Even after the United People's Freedom Alliance (UPFA) government regains control of territory previously held by the LTTE, it is unlikely to restart negotiations with the group.
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