There was no immediate comment from the LTTE.
Meanwhile, in the eastern port city of Trincomalee, the military said police recovered a surface-to-air missile suspected to have been hidden by the rebels.
Ceasefire offer 'hilarious'
Tuesday's offensive comes a day after the LTTE announced it would comply with international calls for a ceasefire, but would not surrender its weapons.
The rebels issued a statement on Monday appealing to international powers to step in and broker a truce.
"The international community must do everything in its power to bring a ceasefire so that the miseries of the Tamils ... are brought to an end," the statement said.
The LTTE said "the international community should apply pressure on the Sri Lankan government to seek not a military, but a political, solution to the ethnic conflict".
But in its statement, the LTTE rejected calls to disarm.
Keheliya Rambukwella, a government spokesman, dismissed the ceasefire offer as "hilarious" and said it comes just as the LTTE is "on the verge of defeat militarily".
The LTTE is fighting for a separate Tamil homeland in Sri Lanka's north, claiming Tamils have suffered years of discrimination by the country's Sinhalese majority.
More than 70,000 people have been killed in the fighting since Sri Lanka's civil war began in 1983.