The military said it had repelled a rebel offensive which broke through army lines in Jaffna on Saturday.
Some 60,000 people have fled the fighting, while another 10,000 are caught between the two sides.
Despite the fighting, senior officials have indicated the government is ready to revive peace talks with the rebels.
The rebels made an offer of talks through the Nordic ceasefire monitoring mission and has been accepted by the government, Palitha Kohona, the chief of the government's peace secretariat said.
Officials were waiting for the Tamil Tigers to respond so that a time and place for the talks could be set, Mr Kohona was quoted as saying by the Associated Press news agency.
On Sunday, the military said the Tamil Tigers had launched a sea attack against islets just south of Jaffna town.
Soldiers called in air support and say they forced the rebels to retreat after 20 minutes of intense clashes.
There has also been heavy shelling close to the dividing lines between government and Tiger-controlled areas of Jaffna.
Thousands of government soldiers are stationed on the isolated peninsula, which is cut off by rebel territory and accessible only by the sea.
Truce monitors, quoted by the Reuters news agency, said they believed the Tamil Tigers were trying to cut supply lines to Jaffna, which has changed hands several times over the past two decades.
The latest fighting follows a day of heavy artillery exchanges during which both sides said they had taken or recaptured territory.
The two sides also blamed each other for sparking the fighting, which the government on Saturday said had left 27 soldiers and more than 100 rebels dead.
As well as Jaffna, Trincomalee in the north-east and Batticaloa in the east saw fighting on Saturday.
Trincomalee was reported quiet on Sunday but local sources said there was fighting around Batticaloa as the army tried to break through Tiger lines.
The flare-up in fighting has alarmed Sri Lanka's key foreign donors who called for an immediate end to the hostilities, which they said was "seriously unravelling" the 2002 ceasefire agreement.
They also expressed serious concern about the humanitarian situation.
There has also been violence away from the front lines.
On Saturday, a senior government peace official, Ketheesh Loganathan, was shot dead in the capital, Colombo.
He was the deputy head of the government's peace secretariat, which co-ordinates the Norwegian-brokered peace process between the government and rebels.
Source:BBCLast Mod: 00 0000, 00:00