Government forces say they are on the verge of defeating the Liberation Tigers of Tamil Eelam (LTTE) after more than 25 years of civil war.
Troops have taken control of most of the Tamil areas across the north of the country, trapping the LTTE in a 100sq km strip of land along the coast.
The government and human-rights groups have accused the LTTE of holding the civilian population hostage, a charge it denies.
In another development, India has offered to aid the evacuation of civilians trapped in the fighting.
Sri Lanka's Tamils share close cultural and religious links with the 62 million Tamils of India's southern Tamil Nadu state.
Emphasising the necessity of a "negotiated political settlement" acceptable to all communities in Sri Lanka, Pranab Mukherjee, India's foreign minister accused the LTTE of inflicting "much damage" on the wider Tamil community.
In the past India trained and armed the Tamil Tigers, but no longer gets directly involved in the politics of the island since a disastrous military intervention in the 1980s when Indian troops, sent to enforce a peace deal on the island, ended up battling the Tigers for 32 months, losing at least 1,200 men in the process.
The LTTE has been fighting for what it calls an ethnic Tamil homelamd since 1983 in predominantly Sinhalese Sri Lanka.