About 30 rebels were killed on Friday in the Puthukkudiriruppu area, the last stronghold of the Tigers, while another two were killed on Saturday, the ministry said.
"Infantrymen further advanced into LTTE (Liberation Tigers of Tamil Eelam) hiding areas...
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inflicting heavy damages to terrorists," it said in a statement.
There was no comment from the Tigers, but the pro-rebel Tamilnet website said 69 civilians, including 19 children, were killed by military shelling in an area designated as a "safe zone" by the government.
Sri Lanka's army denies targeting the "safe zone" and in turn accuses the Tigers of fabricating reports of large scale civilian deaths.
Independent verification of the casualty figures is not possible as the government prevents most journalists, aid workers and international observers from entering the conflict zone.
However the UN human rights chief Navi Pillay on Friday said some 2,800 civilians had been killed in the fighting since January 20, adding