Hugo Chavez
Hugo Chavez is comforted in hospital by his daughters recently. Rumours are swirling that the Venezuelan president has died.

Venezuelan President Hugo Chavez is said by his allies to be "fighting for his life". But some political rivals have claimed he is dead, and the scramble to succeed him as leader of the nation with the world's largest oil reserves has begun.

Vice president Nicolas Maduro said the charismatic and hugely popular socialist leader was undergoing further "intense" treatment at a military hospital in Caracas, while political opponents mounted angry recriminations over the secrecy that surrounds his health.

The president's son-in-law Jorge Arreaza hit out at Chavez's opponents on the right for "launching absurd and bizarre rumours", and insisted the president was "calm" in hospital with his family and doctors at his side.

Chavez's elder brother Adan Chavez, the governor of Barinas state, told supporters: "There he is, continuing his fight, his battle, and we are sure of victory!"

Panama's former ambassador to the Organization of American States, Guillermo Cochez, claimed Chavez died after relatives switched off his life support several days ago. Cochez said Chavez had been in a vegetative state since the end of December, and challenged the president to prove otherwise by showing himself in public.

Supporters attended a mass in the chapel of the Military Hospital Carlos Arvelo in Caracas, where Chavez, 58, underwent treatment, according to state news agency AVN.

Chavez has not been seen or heard from in public since undergoing his fourth operation in Cuba on 11 December. Only a set of photos showing him lying in a Havana hospital bed has been released.

The government has never revealed the nature of Chavez's cancer.

The president returned to Venezuela in late February, more than a month after his inauguration on 10 January, and was readmitted to hospital in Caracas last week without the fanfare that had accompanied previous homecomings.

Vice President Maduro, Venezuela's de facto leader and Chavez's anointed successor, urged the people to stay calm, patient and respectful.

"The treatments Commander Chavez is receiving are tough, but he is stronger than them," Maduro said after the hospital mass.

"He's in good spirits, battling. Leave him in peace. He deserves respect for his treatments, because he's a man who has given everything for our fatherland."

Opposition politicians accuse the government of concealing Chavez's true condition. If Chavez dies or steps down, a vote will be held within 30 days, with Capriles likely to stand against Maduro for the leadership.

"Maduro has lied repeatedly to the president's supporters and to Venezuelans about his real situation," opposition leader Henrique Capriles said. "Let's see how they explain to the nation in coming days all the lies they have told."

Speculation over the president's condition has gripped the 29 million-strong population. Scores of students and activists chained themselves together in a Caracas street, demanding to see the president and protesting against Maduro's succession.

The government said last week that Chavez's breathing difficulties had worsened, and he was using a tracheal tube.

Chavez suffered a severe respiratory infection following the six-hour operation he underwent in December for a cancer that was first detected in his pelvic region in June 2011.

Remarkably, two opinion polls this week showed that a majority of Venezuelans - 60 percent in one survey, 57 percent in another - believe he will be cured.

Last year, Venezuela overtook Saudi Arabia as owner of the world's largest known oil reserves.