Aircraft hit two positions of the Liberation Tigers of Tamil Eelam (LTTE) at Iranamadu, just south of their political capital of Kilinochchi which fell to government forces earlier this month, the ministry said.
"Sri Lanka air force Mi-24 helicopter gunships and fighter jets made precision air assaults against two identified LTTE gathering points located in general area of Iranamadu," the ministry said in a statement.
The ministry said 19 Tiger rebels were killed and many more wounded in clashes in the Kilinochchi district on Sunday.
It did not say if its troops suffered any casualties.
The ministry said last week that security forces were ready to deal a "decisive blow" to the rebels after the capture of the strategic Elephant Pass causeway linking the Jaffna peninsula with the rest of the mainland.
The LTTE's main political headquarters of Kilinochchi town was overrun by government troops earlier this month and the rebels are now confined to the jungle and lagoon distric