Sri Lanka's Tamils share close cultural and religious links with the 55 million Tamils in the southern Indian state of Tamil Nadu.
New Delhi has expressed concern over the conflict, as legislators from Tamil Nadu threatened to resign unless the Indian government took action.
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Basil Rajapakse, a top aide of Sri Lankan President Mahinda Rajapakse, said he had held "very positive" talks with Indian Foreign Minister Pranab Mukherjee.
Rajapakse told reporters after the meeting that he had given India "every assurance" that Tamils' humanitarian needs would be met.
Indian Prime Minister Manmohan Singh is under pressure from the Tamil regional DMK party to halt arms supplies to Colombo and mediate in the conflict.
"The situation in Sri Lanka is of serious concern to the government, in particular the deteriorating humanitarian situation in north of Sri Lanka," Mukherjee told parliament last week.
Singh has asked President Rajapakse to start a peacefully negotiated settlement and