Air raids kill one person and damage a power station and an army base.
However, the Tigers, in remarks published on a rebel-affiliated website, said only seven Tamil suicide bombers had died.
It said that 20 Sea Tiger attack craft took part in the battle.
Jaffna is controlled by government forces, but cut off from the rest of the island by LTTE-held territory and supplied entirely by ship or aircraft.
Eleven days ago, the Tamil Tigers used suicide craft against two merchant ships transporting supplies to the Jaffna peninsula.
The latest fighting came as government security forces continued their ground offensive against the separatists around the northern town of Kilinochchi, their de facto administrative capital.
The government has said it is confident that it will defeat the Tamil Tigers in the north of the island, after more than 20 years of battling the group which wants an independent homeland for ethnic Tamils.
At least one senior government figure has talked of defeating the rebels militarily within two to three years.
The military has stepped up its offensive in the last three months and says it has steadily seized one LTTE stronghold after another and is within striking distance of Kilinochchi.
Tens of thousands of people have died since the LTTE launched its campaign in 1972.