66-year-old Kumaratunga, who was herself seriously injured in an LTTE attack in late 1990s, alleged that some elements in the present government do not understand that Tamils as a population are different from the terrorist organisation, which was militarily defeated in 2009.
She also sees the prevailing environment in the island as a "big window of opportunity" to resolve the decades-old ethnic conflict by addressing their grievances through political means.
"We are concerned that as much as can be done is not being done. Almost three years have passed and we are all very happy that the Tigers, the terrorist organisation has been defeated decisively.
"But what worries me is that some people in the government don`t understand that the terrorist organisation is different from Tamils as a population,? she told PTI in an interview here.
The former President, who is here on a private visit, noted that Tamil civilians have also suffered for almost three decades due to the war and "various forms of discrimination."
"So a lot more can be done for reconciliation, for reconstruction of the damaged structures and reconciliation of the Tamil population with the country," she said.
She was asked whether she was satisfied with the steps being taken by Rajapaksa Government in addressing the ethnic Tamil crisis that had its origins from the sixties and seventies.
To a question whether she expects Rajapaksa to walk the extra mile in achieving political reconciliation with Tamils, she said: Yes, definitely. I walked hundreds of miles and I cleared the way for whoever came and it is not difficult for him to do that."
Kumaratunga, the first woman President of Sri Lanka, said the end of LTTE is "a very big window of opportunity" and noted that India and many other countries have been asking Sri Lanka to give a political settlement to Tamil people.
India has been pushing Sri Lanka to quickly follow-up the military victory against LTTE with a political solution that would address the genuine reconciliation of the minority Tamils.
It also wants the Sri Lankan Government to go beyond the landmark 13th Amendment that envisages devolution of powers to Tamil-dominated areas in addressing the question. To a question whether she saw any possibility of LTTE resurrecting itself, Kumaratunga said: "No, not at all."