CARACAS (AFP) - Somber Venezuelans began 2013 fretting over their ubiquitous and garrulous leader Hugo Chavez, wondering what the future holds as the president wages a tough battle with cancer in a Havana hospital.

Mr Chavez won re-election in October and is supposed to be sworn in on Jan 10, but that seems up in the air now, stoking the prospect of major upheaval in a nation that sits atop the world's largest proven oil reserves.

If Chavez, who has completely dominated Venezuelan political life since taking power in 1999, is declared incapacitated before then - or dies - the Venezuela constitution demands that new elections are called within 30 days.

As Mr Chavez's health crisis has deepened, his handpicked political heir, vice-president Nicolas Maduro, a burly and mustachioed former bus driver and union leader, has been trying to look more prominent and statesmanlike.

But the key question is whether chavismo, Mr Chavez's left-wing movement marked by patronage and generous government handouts to the poor, can survive without him.

If new elections are held, opposition leader Henrique Capriles - who gave the comandante a good run for his money in the October election - might prevail and seek to begin a new era.

For now, both the government and the opposition are leaving open the possibility of postponing the inauguration, depending on how Mr Chavez's health evolves.

Less than two years ago, it would have been impossible to imagine the country without the larger-than-life Chavez at the helm.

His outsized personality and bombastic style of governing did not permit the ascension of an heir apparent within his United Socialist Party of Venezuela.

But before leaving for Cuba in December, Mr Chavez anointed Mr Maduro as his chosen successor and for many that signalled that the process of transition had begun.

Venezuelans began 2013 pondering what political life without Mr Chavez might be like.

New Year's Eve revelry was tempered, and official acts - two open air concerts - were canceled outright out of respect for the ex-paratrooper who has irked the United States for years by aligning his country with such countries as Iran, Cuba and Syria.

Mr Chavez underwent his fourth cancer-related surgery three weeks ago in Havana and has been bed-ridden ever since. Information on his condition is scant, with the government admitting only to "complications" in his recovery.

The streets of Caracas were practically deserted early Tuesday.

"You can feel the sadness in the air. People are sorry about what is happening with Chavez," said a doorman who gave his name as Adrian, alluding to the toned-down parties of the night before.

"I hope we will have a better year in 2013. Nothing will be the same without Chavez, no matter who the next president is." Elsewhere in Latin America, leftist allies expressed hope for, and even prayed for, Mr Chavez's recovery.

"I am very sorry that our Latin American brother Hugo Chavez, our comrade in the fight, an anti-imperialist comrade, a revolutionary, is facing such a difficult situation regarding his health," said Bolivian President Evo Morales.

In Venezuela, Twitter has been red hot with comments and rumours to the effect that Mr Chavez, the tough-talking 58-year-old face of the populist left in Latin America, is fading fast or even dead already.

From Havana, Science and Technology Minister Jorge Arreaza - the president's brother in law - fired back, seeking to restore calm.

"Countrymen, do NOT believe mean-spirited rumours." Mr Arreaza tweeted.

"President Chavez spent the day quietly and in stable condition, in the company of his children," the minister wrote on Monday evening.

Even Capriles, the young opposition leader, warned Venezuelans to stay away from rumours.

"Let us not fall victim to the trap of rumours and hatred," Mr Capriles tweeted. "Let's spend energy on building, not destroying." Since Mr Chavez left for Havana more than three weeks ago, he has not appeared in public, nor have photos of him been published - something highly rare for a man who is usually all over the media in one form or another.

Mr Chavez had declared himself cancer free in July, more than a year after being diagnosed with the disease in the pelvic region. The exact nature of the cancer has never been made public and no official medical report has been released.