Rebel leader Prabhakaran was hiding near the coast, Lt Gen Fonseka said.
Troops believe he could try to escape the war zone by boat, a method used by other rebel leaders.
There is no media access to the area, so it is difficult to interpret the parallel propaganda war, says the BBC's Charles Haviland in Colombo.
The general said only 300-400 Tamil Tiger fighters remained, but there may be 700 "forcibly armed" people in rebel bunkers.
TAMIL TIGER DEFENCES BREACHED BY SRI LANKA ARMY
12km-long defensive earthworks constructed by Tamil Tigers using mechanical diggers
Sri Lankan army uses explosives to destroy a 3km section
Gap allows thousands of refugees to flee Tiger-held territory
"We went in and people came towards us and we rescued them and [have] taken them to a better location."
He dismissed any suggestion that international assistance would help resolve the conflict.
Brig Nanayakkara said: "This is our problem and we will sort out our problem."
Sri Lankan President Mahinda Rajapaksa also rejected international offers, telling British Prime Minister Gordon Brown that there was no need to send a special envoy and a pause in fighting was not necessary.
"President Rajapaksa observed that this movement of civilians had evoked a completely new situation and he had instructed that additional consignments of food, medicine and other essentials be dispatched," a government statement said.
Gordon Weiss, the UN spokesman in Sri Lanka, said it was not known how many civilians remained there but that the UN had been working off a figure of some 150,000 to 200,000 people in recent months.
The International Committee of the Red Cross (ICRC) said it was "extremely worried" about civilians still trapped in the zone.
"The situation is nothing short of catastrophic. Ongoing fighting has killed or wounded hundreds of civilians who have only minimal access to medical care," said director of operations Pierre Kraehenbuehl.
The rebel TamilNet website said the territory they still controlled was littered with bodies of civilians.
Video released by Tamil supporters shows mutilated bodies, but it is not clear when the recording was made.
They said it was filmed on Monday, but this cannot be verified.
It follows footage released by the government showing civilians fleeing the war zone.
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