More than 4,800 people have been killed in the latest upsurge of fighting that began in December 2005.
Troops on Thursday recovered bodies of six of the members of the Liberation Tigers of Tamil Eelam (LTTE) in the Madhu area, about 260 kilometres (162 miles) north of Colombo, the ministry said.
"Since yesterday, 20 LTTE terrorists were killed during conflict with troops," the ministry said in a statement. There was no immediate word from the Tigers.
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The military claims came after the army said that Tiger rebels shelled military positions along their de facto border in northern Sri Lanka Thursday, prompting the closure of the frontier post into rebel-held territory.
The Omanthai check point, which is at the entrance to the northern Wanni region that is dominated by the LTTE, closed indefinitely following Thursday's shelling, the army said in a statement.
"The closure will remain until the ground situation returns to normality," the statement said.
Government forces and the rebels