A deadline for the Liberation Tigers of Tamil Eelam (LTTE) to surrender or face a final assault expired at 0630 GMT on Tuesday with no word from the Tigers.
However, hours later a rebel official vowed to continue the battle.
"LTTE will never surrender and we will fight and we have the confidence that we will win with the help of the Tamil people," Seevaratnam Puleedevan told Reuters news agency.
The head of the Sri Lankan army, Lt Gen Sarath Fonseka, told the BBC Sinhala service that troops know the "general area" of Tamil Tiger leader Velupillai Prabhakaran and that "action will be taken to destroy him".
This is our problem and we will sort out our problem.
"We do not know exactly the place where he is hiding, but we suspect he is most probably hiding among the civilians, trying to take cover behind them.
"Therefore we have to be very careful about what action we take to ensure that no civilians get harmed."
Rebel leader Prabhakaran was hiding in coastal strip about 8km long and 1.5km wide, 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.
Sri Lankan military spokesman Brigadier Udaya Nanayakkara told the BBC's Newshour programme that the army had rescued the civilians after breaking down earthen defences, rather than forcing them to flee amid fighting, as suggested by the rebels.
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, where they can have a better life than what they had in this safety zone under the LTTE [Tamil Tiger rebels]."
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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