They said villagers found blood and three identity cards belonging to the missing men.
The defence ministry said it had no information about the Tiger allegations but said that in the country's east, troops and Tamil Tiger rebels traded mortar and automatic rifle fire on Sunday.
"There are no casualties among troops but we don't know if there are any on the other side," the spokesman said, adding that the firefight around the Vavunathivu military base lasted nearly two hours.
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A soldier was wounded when suspected Tiger gunmen fired at a sentry point in the same region on Sunday morning, the spokesman said.
The latest attacks came as Japanese envoy Yasushi Akashi met Palitha Kohona, head of the government's peace secretariat which coordinates the Norwegian-backed peace initiative.
Akashi