It said their "only way out is to surrender to the security forces or to be crushed in the military advance."
The defence ministry said it also believed the leader of the Liberation Tigers of Tamil Eelam (LTTE), Velupillai Prabhakaran, was still holed up in the area.
A defence spokesman said earlier that the massive Sri Lankan government offensive against the Tamil Tigers will be over "very soon" with the army on the brink of capturing the last rebel-held territory.
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"The fighting has come to the last stage of defeating terrorism," said Lakshman Hulugalle, the director general of the defence ministry's Media Centre.
"We expect the good news of ending the fighting very soon."
Sri Lankan state television, which has reporters at the frontline in the northeast, sa