Samarasinghe also said there were plans to provide surrendering fighters vocational training to help them reintegrate into society.
Tamil Tiger leaders have vowed never to surrender, and every fighter is said to wear a cyanide capsule and sworn to swallow the capsule to avoid capture.
But the government said a number of fighters have already given themselves up, including the former LTTE media spokesman and an interpreter for its political wing.
The amnesty proposal comes as Sri Lanka's military accused the LTTE of fabricating images purportedly showing the aftermath of a deadly attack on a hospital in the conflict zone.
The photographs, first published on a pro-LTTE website, depicted what Tamil separatist sources said was an artillery hit on a makeshift hospital in Mullivaikal on Saturday.
The website alleged that government sources had killed 81 people after two consecutive days of shelling.
Al Jazeera's David Chater, reporting from Colombo on Sunday, said Sri Lankan military experts "have analysed the pictures and claim they were deliberately posed for propaganda purposes".
"Their analysis: 'Not a single scratch mark on the fridge with a body lying at its base, unbroken glass bottles and no pellet marks on the walls, a bottle remains steady on the stretcher, all after the claimed shelling'," he said.
"The message, the government says, is clear: The foreign media have been taken for a ride by the Tamil Tigers."
Brigadier Udaya Nanayakkara, Sri Lanka's military spokesman, said over the weekend that the claims were the latest in a series of "exaggerated stories" by those sympathetic to the LTTE.
"There is no shelling taking place; we have never shelled this place and it happened in an area where the LTTE [are in control]," he told Al Jazeera.
It is impossible to independently verify reports from the army or LTTE due to journalists and international organisations being barred from the war zone.
The conflicting reports come as Tamil Tigers continue to urge Britain and France to press the Sri Lankan government into calling a ceasefire.
In letters sent on Sunday to David Miliband and Bernard Kouchner, the British and French foreign ministers, Balasingham Nadesan, the political leader of the LTTE, said the group was ready to "engage in the process to bring about a ceasefire".
Nadesan said they were ready to "enter into negotiations for an enduring resolution to the conflict".
Miliband and Kouchner visited Sri Lanka last week and urged the military to halt fighting and allow humanitarian aid into the northeastern coastal conflict zone.
|The UN estimates up to 50,000 civilians
still remain in the war zone [Reuters]
The move came amid growing international concern over the plight of civilians trapped in the 5km strip of land controlled by the LTTE.
The Sri Lankan government has rejected a call for a truce from the LTTE, demanding the rebels surrender or face defeat.
Thousands of people have fled the area but the UN has said that up to 50,000 civilians could still be trapped.
Many of the refugees who fled the area were badly wounded or ill and seemed to confirm government accusations that the Tigers were holding them against their will and using them as human shields.