Ratnasiri Wickremanayake told parliament that Prabhakaran, 54, was still leading his Liberation Tigers of Tamil Eelam (LTTE) fighters in their desperate battle for survival against an overwhelming military offensive.
"We have information that Prabhakaran is still in a four-square 1.5 square mile area in Mullaittivu," Wickremanayake said in reply to a question about the elusive Tiger leader.
He said the guerrillas still had a large arsenal of weapons, with which they were fighting back against government troops.
Prabhakaran has not been seen for more than 18 months, and speculation has been rife that he may have been killed or already fled the island.
Sri Lanka´s navy has increased patrols off the Mullaittivu coast to stop him escaping, and Malaysia and India have been alerted to be on the lookout.
Government soldiers trying to end Prabhakaran´s 37-year violent campaign for an independent Tamil homeland have attacked the final patch of rebel-held territory from a new direction, the defence ministry said on Tuesday.
"Troops commenced advancing northwards from the initial forward defenses at Wadduvakal," the ministry said, adding that the guerrillas were putting up stiff resistance.
Recent military attacks into the territory have been from the north.
The ministry said troops were progressing with "utmost restraint" to prevent deaths among tens of thousands of civilians being held hostage by the Tigers.
"Terrorists have suffered heavy beating from the security forces and are now left in total disarray," the ministry said. It gave no details of casualties in the latest fighting.
The Sri Lankan government has been saying for months that it is about to completely crush the separatist fighters and "free" the trapped civilians.
With victory apparently imminent, President Mahinda Rajapakse has said he wants Prabhakaran to be taken alive.
The United Nations, which says thousands of non-combatants have been killed in fighting this year, has led international calls for the Sri Lankan government to agree to a ceasefire to prevent further bloodshed.
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