State TV broadcast images of the corpse of 24-year-old Charles Anthony, Prabhakaran's son and heir apparent, on Monday.
The senior LTTE officials found dead include Balasingham Nadesan, the head of the political wing, Seevaratnam Puleedevan, and S Ramesh, the separatists' eastern leader, Brigadier Udaya Nanayakkara, a military spokesman, said.
There has been no comment from the LTTE on the latest claims.
Al Jazeera's Tony Birtley said: "The conventional guerilla fighting forces of the Tamil Tigers is probably now finished, what happens now is the big question.
"Depending on what happens in the peace process the fear is that this may actually develop into guerilla war again ... but what about the peace? Who’s left to talk to? There is not many left to talk to.
"A lot of mistrust has developed over the years; I think that's the reason why this conflict began in the first place. Now it's a problem that both sides have to make themselves understood."
The military has refused to accept a ceasefire from the Tamil Tigers group, which a day earlier laid down its arms and declared that its 26-year battle with the government had come to a "bitter end".
Selvarasa Pathmanathan, the Tigers' international spokesman, said: "We have decided to silence our guns."
The army said it would continue its offensive and described Monday's activities as "mopping up" operations.
Keheliya Rambukwella, a defence ministry spokesman, told Al Jazeera on Monday that the government had "had enough of ceasefires".
"As usual they [Tamil Tigers] are going to strengthen and rearm themselves," he said.
The government will accept a ceasefire only if it helps civilians, he said.
The government maintains that the tens of thousands of civilians who had been trapped in the small area of conflict had finally been able to leave on Sunday.
Sri Lanka says it will now kill or capture remnants of the LTTE army, with an intensive search under way for Prabhakaran.
Minelle Fernandez, reporting for Al Jazeera from Colombo, said: "Reports have indicated that leader Velupillai Prabhakaran has been killed, there are somewhat conflicting reports about how this happened.
"There are stories that the army fired an RPG at a vehicle carrying Prabhakaran and two other senior leaders and there are reports that he was shot while fleeing.
If he is confirmed to have been killed it would "spell the end of the organisation that has been built almost around the cult Prabhakaran", she said.
"It is a surprise that it has fallen and literally brought to its knees and been defeated this quickly.
'Conflict not resolved'
Far from the battlefield, thousands of Sri Lankans hugged soldiers, waved flags, set off firecrackers and danced to the beat of traditional drums in the streets of the capital, Colombo, celebrating the end of more than 25 years of conflict.
Despite the government's apparent crushing military victory against the Tigers, Erik Solheim, a Norwegian minister and former negotiator in the conflict, warned on Sunday that "peace is long from being won".
"The Sri Lankan authorities must demonstrate generosity towards the Tamil population and grant Tamils autonomy and create a state that includes everyone," Solheim, who is Norway's international development and environment minister, said.
|Puleedevan was among the senior officials reportedly killed by the army [AFP]
"The conflict is not resolved even if the battle has been won."
Norway helped broker a ceasefire in February 2002, which came to an end in October 2006 when peace negotiations broke down.
Pathmanathan, the Tigers' spokesman, said bodies of thousands of wounded and slain civilians remain in the war zone.
The Sri Lankan ministry of disaster management and human rights said on Sunday that it was continuing to process civilians rescued from the fighting.
Rajiva Wijesinha, a secretary at the ministry, told Al Jazeera from Colombo: "We heard that the last of them [civilians] had been saved. This was one of our great priorities in the last couple of weeks to make sure we got the civilians safely away."
The government and the Tigers alike have been criticised for not allowing civilians to safely leave the area and for precipitating a humanitarian disaster.
More than 70,000 people have been killed in the conflict that started in 1983 and the UN says 6,000 were killed and hundreds of thousands displaced in just the last four months.
'Struggle to continue'
The Tamil Tigers once controlled nearly a fifth of the Indian ocean island nation, running a shadow state that had courts, police and a tax system along with an army, navy and even nascent air force.
But by Sunday, government troops had surrounded the remaining fighters in a one sq km patch of land and were seeing suicide bomb attempts and plain suicides by fighters, the military said.
However, the struggle for a homeland for ethnic Tamils who say they are marginalised by the ruling majority Sinhalese government would continue, Rajavarothiam Sampanthan, the leader of the Tamil National Alliance, told Al Jazeera.
"The Tamil struggle started long before the Tigers were born and will continue after the end of the Tigers," he said from Chennai in India.
"The Tamils have always demanded self-determination, which would mean substantial self-rule in the areas of their historical habitation."