Selvarasa Pathmanathan, the international spokesman for the group, admitted that many senior members had either "given up their lives or have been treacherously killed", but insisted that Prabhakaran was "alive and well".
"Our beloved leader is alive and safe. He will continue to lead the quest for dignity and freedom for the Tamil people," Pathmanathan said in a statement on the pro-LTTE website TamilNet.
Sri Lankan military sources had earlier said that Prabhakaran's body had been found in an ambulance destroyed by troops as it sped out of the war zone. But Tuesday's official account contradicted those claims.
The developments came amid a parliamentary address by Mahinda Rajapaksa, Sri Lanka's president, officially declared victory over the LTTE, saying the country had been "liberated from terrorism".
He said the government controlled "every inch" of Sri Lanka for the first time after more than 25 years of civil war.
Delivering his speech partly in the Tamil language, Rajapaksa said the war was not waged against the country's Tamil minority.
"Our intention was to save the Tamil people from the cruel grip of the LTTE. We all must now live as equals in this free country," he said.
Rajapaksa congratulated his military commanders on Monday and promised a power-sharing deal with the Tamils.
Jehan Perera, executive director of the National Peace Council of Sri Lanka, said that the country is now in a position to move forward.
"The president has a lot of credibility. He is trusted by the Sinhalese people so he has a great opportunity to make the compromises and accommodations necessary to reach out to Tamils and satisfy their long-standing demands," he told Al Jazeera.
"There's a sense among Tamils that there's no one to speak for them, that they have lost everything and gained nothing. I think the government has to make some symbolic gesture towards the Tamils and change things on the ground."
The Tamil Tigers had been fighting with the stated aim of carving out a separate homeland for ethnic Tamils in the country's north and east.
They accused the Sinhalese-dominated government in Colombo of neglecting Tamils.
The LTTE once controlled nearly a fifth of the country, running a shadow state that had courts, police and a tax system along with an army, navy and even a nascent air force.
But on Sunday, the group said it would "silence [its] guns", declaring that its battle with the government had come to a "bitter end".
The Rajapaksa government faces scepticism that it will be genuinely inclusive now that it has defeated the LTTE.
It also faces a looming humanitarian crisis, with the UN estimating that 8,000 people were killed and about 250,000 displaced in just the last four months of the conflict.
The government and the Tamil Tigers alike were criticised for not allowing civilians to leave the conflict zone and firing on them.
UN officials say Ban Ki-moon, the secretary-general, is expected to visit Sri Lanka this week, where he will focus on trying to help the displaced, pressing for their speedy return home.