Rasiah Ilanthiriyan, the Tiger spokesman, said in a statement: "The Sri Lanka armed forces fighting units are already beaten back in two of the three fronts.
"The two sides use heavy artillery, multi-barrel rocket launchers and small mortars to provide tactical support fire to respective troops. The shelling duel and firefights still continue in those areas."
Both sides regularly make sharply differing claims about casualties and independent verification is rarely possible.
Journalists are also not allowed access into areas in the north held by the separatist group.
Sri Lanka is pressing for a military victory over the group which is fighting for a separate state for the ethnic Tamil minority in the Sinhalese-majority nation.
Tens of thousands have died on both sides since the conflict started in 1972.
The latest casualty claims by the military bring the number of Tamil fighters killed since December 1 to at least 535, according to the defence ministry.
This compares with less than 30 troops reported dead or missing by the military.