Marulanda has led the Farc since it was formed 44 years ago
The Colombian military says the top commander of the country's largest rebel group, the Farc, has died.
A national news magazine had earlier reported the death of Manuel "Sureshot" Marulanda on 26 March after bombing raids by the Colombian air force.
There has been no confirmation from Farc sources. Mr Marulanda's death has been rumoured and disproved before.
Meanwhile, President Alvaro Uribe said some rebels were ready to surrender themselves and some key hostages.
He said he had received "calls" from Farc leaders who said they were ready to hand over hostages, including former presidential candidate Ingrid Betancourt, and leave the guerrilla force if their freedom could be guaranteed.
But Mr Uribe, whose popularity is riding high in Colombia because of his hard-line campaign against the Farc, added that some commanders were determined to fight on.
On the question of Mr Marulanda's reported death, Mr Uribe was cautious, saying only that the information came from sources that "have been serious, let's wait."
Correspondents say the death of Mr Marulanda, if confirmed, could even threaten the Farc's future existence.
Mr Marulanda, whose real name is Pedro Antonio Marin, has led the Revolutionary Armed Forces of Colombia, or Farc, since its foundation in 1964.
He is thought to be 78 years old and there have been persistent rumours of ill health, including evidence that suggested he had prostate cancer.
A statement from the head of the Joint Chiefs of Staff, Admiral David Rene Moreno, said it was not yet confirmed how Mr Marulanda died.
He said three bombing raids by government forces had targeted the area where Mr Marulanda was believed to have been staying, but not on the date he is reported to have died.
Admiral Moreno added that the version among the Farc rebels themselves was that their leader died from a heart attack and they have designated a political leader known as Alfonso Cano as his successor.
"If they are going to say that the information we have is not correct, then let them prove it," he said.
"Whether Marulanda died in an air raid or of natural causes, this would be the hardest blow that this terrorist group has taken, since 'Sureshot' was the one who kept the criminal organisation united."
The BBC's Jeremy McDermott, in Bogota, says the 44-year-old rebel movement is currently suffering its worst period yet, with two top commanders dead and others surrendered.
Farc holds scores of people hostage in jungle bases, including Ms Betancourt, who was abducted during the presidential campaign in 2002.