The Tigers on Monday said that they killed more than 100 soldiers and had taken back territory lost to advancing government forces.
Both sides are known to make exaggerated claims about casualties they have inflicted on each other, and independent verification is virtually impossible as journalists and aid workers are barred from the conflict area.
The rebel Liberation Tigers of Tamil Eelam (LTTE) mounted the offensive outside their besieged political capital of Kilinochchi on Wednesday, the ministry said.
"Well prepared troops engaged the advancing terrorists with armour, tanks, artillery and infantry causing heavy damage," the ministry said in a statement.
It said 18 rebels were killed and another 34 wounded, but did not give details of casualties on the government side.
The pro-rebel Tamilnet.com website said there was heavy fighting in the area, but gave no further details.
Military officials said war planes also carried out bombing missions against Tiger defences o