The offer comes two days after Tamil Tigers used at least one light aircraft to bomb a Sri Lankan air force base outside Colombo, the capital, in the separatists' first air attack since they started their campaign for a homeland for the country's Tamil minority in 1983.
Three airmen were killed in the attack and 16 people wounded. No aircraft on the ground were damaged.
Apart from suicide bombings carried out by the Tigers, almost all the fighting in the two-decades long conflict has taken place in predominantly Tamil regions in northern and eastern Sri Lanka.
But the air raid has showed the rebels can now strike inside the southern heartland of Sri Lanka's Sinhalese majority.
Air force fighters also bombed three Tamil Tiger fighter positions in the northeast on Tuesday, according to Group Captain Ajantha Silva, an air force spokesman.
"Hopes for peace that followed a 2002 ceasefire have been dashed by shootings and bombings over the past 18 months"
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There was no information on damage or casualties.
Ban Ki-moon, the UN secretary-general, has called on the two sides in a statement to "break this vicious cycle of attack and retaliation" and "return to the negotiating table as soon as possible, without preconditions".
In the years since the Tamil Tigers began their fight for independence for the country's three million Tamils, they have pioneered the use of suicide bomb belts and built up a navy of small gunboats.
Hopes for peace that followed a 2002 ceasefire have been dashed by shootings and bombings over the past 18 months.
An estimated 65,000 people were killed in fighting before the cease-fire, and an estimated 4,000 fighters and civilians have died in the last 18 months.
A military foot patrol shot and killed two Tamil Tiger fighters on Tuesday in northwestern Mannar, the defence ministry said on Wednesday.
Earlier on Tuesday, a fighter drove an explosive-laden tractor to the Chinkaladi military camp in the eastern district of Batticaloa, drawing fire from guards and triggering a blast.
The resulting explosion killed the tractor's driver, three soldiers and five civilians and wounded 20 people, a Sri Lankan military spokesman, said.