Palitha Kohona, head of the government's peace secretariat, said that the offer was received through truce monitors on Friday, shortly before fighting erupted on the northern Jaffna peninsula.
"There had been no contact since," he said.
"A message was received that the Tigers offered peace talks and we accepted."
"The Tigers also wanted to know if there were any conditions. We said there would be no conditions but since then there had been no response," he said.
Meanwhile the fighting in the north east of the country continued in what have been the fiercest clashes since a truce was brokered in 2002.
"I believe that the offer is based on some comments made by Sri Lankan officials. The LTTE has not given any reponse," Ove Jansson, head of Trincomalee district for the Nordic-backed Sri Lankan Monitoring Mission told Aljazeera.
"The north east is geographically very important for the LTTE, it is part of their so-called homeland. I don't believe they are going to give up easily," said Jansson.
Jansson told Aljazeera that he was particularly worried about Tamil residents trying to flee the fighting, which has broken out around Batticaloa and Muhamalai, a strategic point which lies on the only highway that heads into the core of the peninsula.
"I believe that the checkpoints at Vakari have been closed, which means there are thousands of people trapped in the conflict zone"
head of the Trincomalee district Sri Lankan Monitoring Mission
"I believe that the checkpoints at Vakari have been closed, which means there are thousands of people trapped in the conflict zone," Jansson said.
Fighting rages on
On Saturday the Tigers' leadership said they had pushed through a no-man's land separating rebel and government territory, destroying army checkpoints on the other side, and were advancing along the main road that connects the peninsula to their territory.
"We have completely destroyed the army checkpoints at the Muhamalai [border] crossing, and we are advancing on Jaffna," a Tiger official at the rebel Voice of Tigers radio station said. However, military officials said they had pushed back a rebel offensive on Sunday.
He said the separatists' Sea Tiger wing had attacked south of Jaffna town and struck a navy base at the island's northern tip before dawn on Saturday.
A military statement said that 27 of its personnel had been killed and 80 injured in the current clashes and estimated it killed more than 150 separatist fighters.
The military said that it sank the five Sea Tiger boats as they attacked military posts on the shore of Jaffna.
"The government's military campaign against the rebels is "mollycoddling" the LTTE"
Kethesh Loganathan, deputy head of the government peace secretariat
Residents who live along the path of the Tiger advance had been told to leave immediately.
Killings and attempted assassinations in the island's south, well away from the front lines, have accompanied the fighting.
Kethesh Loganathan, the deputy head of the government peace secretariat, an ethnic Tamil, was gunned down in the capital, Colombo on Saturday evening. He died overnight in hospital.
The government blames the rebels, who have long targeted dissenting Tamil voices.
Loganathan supported the government's military campaign against the rebels and last week told Reuters the international community was "mollycoddling" the LTTE.
Two civilians died when a car bomb
exploded in the capital last week
Most diplomats had blamed the Tigers for an escalation of violence this year that killed more than 800 people even before ground fighting began. But many now blame the government for triggering all-out war by over-reacting to the water dispute.
The eastern port of Trincomalee came under heavy artillery bombardment from Tamil Tiger fighters on Friday which is used to supply the Jaffna peninsula.
The Tigers had claimed government troops were trying to cross a "border" into their territory and that hundreds of civilians were fleeing from army shelling.
"They are firing artillery and trying to breach our borders," a Tiger military spokesman said from the northern rebel town of Kilinochchi.
"We have no details of any break through the lines," said Robban Nilsson of the Nordic ceasefire monitoring mission, adding that the fighting on new fronts in the north and east was alarming.
The government has said it will not halt operations in the north until it controls a disputed waterway in the east and an irrigation reservoir that feeds it - which started the fighting in the first place 18 days ago, and put an unofficial end to the ceasefire which has been in place since 2002.
Many analysts believe that the recent crisis has been triggered by the government's heavy-handed approach to resolving the water dispute.
Sri Lanka's Tamils consider Jaffna their cultural homeland. The Tamil Tigers began fighting in for a separate homeland for the country's 3.2 million Tamils in 1983.
The Sri Lankan military has announced an indefinite curfew in Jaffna keeping shops closed people in their homes.