"During the whole incident, troops attacked the terrorists in retaliation causing them heavy casualties, killing over 40 Tiger cadres and wounding 70 other terrorists," the ministry said in a statement.
The military's claims of rebel deaths could not immediately be confirmed.
It said three sailors were killed and six others were wounded in a clash at the Muttur jetty, while a Tiger shell hit the main hospital in Muttur, killing two civilians, one of them a hospital worker.
In a Tiger shelling of three military camps guarding Muttur, two soldiers were killed and 24 were wounded, the ministry said.
The pro-rebel website Tamilnet said four soldiers were killed and three injured but did not say if the Tigers had suffered any casualties.
During the two-hour shelling by the Liberation Tigers of Tamil Eelam (LTTE), the security forces had retreated from posts in the town centre to bomb shelters but later resumed their positions, the ministry said.
"Ground troops at present c