Several ground battles also saw 25 rebel fighters being killed on Friday morning, the Reuters news agency reported.
Highly varied casualty figures stated by either side cannot be independently verified.
The attacks came a day after the Tigers made an offer to maintain the 2002 ceasefire and asked for peace mediation by Norway.
Ceasefire rejected
The offer was rejected on Friday, with the government promising to eliminate the group.
Keheliya Rambukwella, a minister and government defence spokesman, said: "While the CFA [ceasefire agreement] was on they attacked civilian targets.
"So what they are trying to do is take cover under this and then unleash terror activities.
"We will be going on with our liberation operations. We need to liberate the whole country from terrorism.
"We will flush them out."
The government formally pulled out of a 2002 ceasefire last week.