European Union foreign ministers meeting in Brussels have condemned civilian casualties from the conflict and called for an inquiry into alleged war crimes by both sides.
UN Secretary General Ban Ki-moon's office said he was planning to visit Sri Lanka, without providing any further details.
UN humanitarian aid chief John Holmes said the priority was to evacuate all the civilians caught up in the fighting.
"[We] hope that all the civilians are indeed out of that zone, and indeed are heading towards safety, but it's hard for us to be absolutely sure about that for the moment," he said.
'Alive and well'
Over the past few weeks Sri Lankan forces routed the rebels, overrunning their territory.
The BBC's Charles Haviland, in Colombo
There is jubilation in the streets as crowds cheer, light firecrackers and wave the national flag to greet the announcement from the army chief, Gen Sarath Fonseka, that "all military operations have come to a stop".
In the old bazaar area, Sinhala, Tamil, Muslim and other people told the BBC they were relieved.
For decades they had feared boarding buses or visiting temples, some said, for fear of bombs.
Now they hoped there would be peace with development.
There's still widespread humanitarian concern about civilians who may have been caught up in the fighting.
The Tigers, or LTTE, were eventually cornered in a tiny part of the 15,000 sq km territory they had controlled until recently.
They declared a ceasefire on Sunday.
Military officials said Prabhakaran had been killed along with his intelligence chief Pottu Amman and Soosai, the head of the rebels' naval wing.
They were trying to flee advancing government troops when their vehicle was ambushed, the officials said, adding that the rebel leader's burnt body had been recovered and that DNA tests were under way.
But Tamilnet, the Tamil news service often used by the rebels to issue statements, is running a denial of Prabhakaran's death.
He is "alive and well", it quoted Selvarasa Pathmanathan, the Tigers' head of international relations, as saying.
Ethnic Tamils have demonstrated in London, Brussels and Geneva in protest at Sri Lanka's actions.
Sri Lanka's military also reported killing three other senior rebel leaders, including Prabhakaran's eldest son Charles Anthon, and said it had killed 250 Tamil Tigers on Sunday night.
Under Prabhakaran, the Tigers assassinated several Sri Lankan political leaders and the former Indian Prime Minister, Rajiv Gandhi.
The LTTE was branded a terrorist organisation by many countries and Prabhakaran was wanted by Interpol - the global police network - for murder, terrorism, organised crime and conspiracy.
The government's information department sent news of Prabhakaran's death by text message to mobile phones across the country, prompting celebrations in the streets of the capital Colombo.
Born November, 1954
1972: Founded Tamil New Tigers (TNT), forerunner of LTTE
As the military announced a successful end to their operations against the rebels, President Mahinda Rajapakse was shown on TV shaking the hands of the heads of the three armed services.
National flags have been flying off the shelves, the BBC's Charles Haviland reports from Colombo.
More than 1,000 Sri Lankans also protested outside the British High Commission, accusing the UK of seeking to help the rebels by earlier calling for a ceasefire.
Some protesters threw stones and burnt an effigy of UK Foreign Secretary David Miliband, and a High Commission spokesman said it was "an outrage" that the Sri Lankan authorities had let the demonstration become so violent.
There is still widespread international concern about civilians who may have been caught up in the fighting.
Sources in the UN say significant numbers of civilians were still in the combat zone but the Sri Lankan government said all civilians had left.
The Tigers had been fighting for a separate state for Tamils in the north and east of Sri Lanka since the 1970s.
More than 70,000 people have been killed in the conflict and thousands displaced.
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