* Inauguration delayed as Chavez stays in Cuba hospital
* Supporters plan big rally in streets round palace
* Opposition urges foreign dignitaries to stay away
CARACAS, Jan 10 (Reuters) - Venezuelan President Hugo Chavez remained on his sickbed in Cuba on Thursday while supporters planned to rally in his honor on the day he should have been sworn in for a new six-year term in the South American OPEC nation.
The postponement of the inauguration, a first in Venezuelan history, has laid bare the gravity of Chavez's condition after complications from a fourth cancer operation in his pelvic area.
It has also left his chosen heir, Vice President Nicolas Maduro - a former bus driver who shares his boss's radical socialist views - in charge of day-to-day government until there is clarity over whether Chavez will recover or not.
"People traveling on foot, the humble, the patriots ... tomorrow we're going to demonstrate, one proud people with one slogan: we are all Chavez!" Maduro said in a televised cabinet meeting late on Wednesday.
The president, whose legendary energy and garrulous dominance of the airwaves had often made him seem omnipresent in Venezuela since 1999, has not been seen in public nor heard from since his surgery on Dec. 11.
Venezuela's 29 million people are anxiously watching what could be the last chapter in the extraordinary life of Chavez, who grew up in a rural shack and went on to become one of the world's best-known heads of state.
The saga also has huge implications for the likes of Cuba and other leftist allies who have benefited for years from Chavez's subsidized oil and other largesse.
A clutch of foreign friends, including the presidents of Uruguay, Bolivia and Nicaragua, were due at Thursday's events in Caracas despite Chavez's absence.
Government officials have called supporters to the streets around the presidential palace. It has been the scene of some of the biggest dramas of Chavez's rule, from protests in 2002 and a coup that toppled him briefly, to speeches after election wins and emotional returns from previous cancer treatments in Havana.
"Take your songs, take your banners, so everyone knows we are all behind Chavez in this revolution," Diosdado Cabello, the head of Congress and a close Chavez ally, urged the president's supporters.
'WHO WINS FROM CONFLICT?'
Venezuela's opposition leaders are furious at what they see as a Cuban-inspired manipulation of the constitution by Maduro, Cabello and other Chavez allies aimed at preventing the naming of a caretaker president due to Chavez's absence on Thursday.
Henrique Capriles, who lost October's presidential election to Chavez, said the opposition had no plans to risk violence by encouraging supporters to hold a counter-demonstration.
"Not calling people onto the streets is not a sign of weakness, but of responsibility," he told reporters. "Who wins from a conflict scenario? They win, the pseudo-leaders who are not the owners of the country, nor of its sovereignty."
The U.S. Embassy in Caracas advised American citizens in Venezuela to exercise caution during the next few days.
A top Venezuelan military officer told state TV the borders were being reinforced and security forces were patrolling intensively to bring people "a sense of peace and tranquility."
With government updates short on details, little is known about Chavez's actual medical condition and rumors are flying.
On Wednesday, the state telecommunications regulator told opposition TV station Globovision it was beginning punitive administrative proceedings against it for "generating anxiety" with its coverage of the president's health.
The government's version is that Chavez suffered complications including a severe lung infection after the latest surgery. But speculation is rife on Twitter that he may be on life support or at risk of major organ failure.
He has undergone four operations, as well as weeks of chemotherapy and radiation treatment, since being diagnosed with an undisclosed type of cancer in his pelvic area in June 2011.
He looked to have staged a remarkable recovery from the illness last year, winning a new six-year term in a hard-fought election in October. But within weeks of his victory he had to return to Havana for more treatment.
'REVOLUTION MUST CONTINUE'
In contrast with previous trips to Cuba, the government has not released any photos or video of him recuperating, and Chavez has not made any phone calls home to state media, fueling the impression that his condition is dire.
Though supporters maintain vigils and express hope he will recover, there appears to be a growing acceptance he may not, and a slow adjustment to the idea of a post-Chavez Venezuela.
"We are all necessary but nobody should be irreplaceable and the revolutionary process in our America must continue," said one friend and close ally, Ecuador's President Rafael Correa.
Though often viewed in the West as a clownish autocrat, Chavez has a kinder image in developing nations where many admire his defiance of the United States and efforts to improve the lives of Venezuela's poor.
At home, Chavez has a cult-like appeal for many in the slums due to his "anti-imperialist" rhetoric, his pumping of crude oil revenue into welfare projects, and his own humble background.
But Venezuela is deeply split, with opponents saying he has squandered an unprecedented bonanza of oil money with misguided policies. They also accuse him of allowing corruption to flourish and oppressing political opponents and media critics.
Should Chavez die or step down, a new election would be called and it would likely pit Maduro against opposition leader Capriles, the 40-year-old governor of Miranda state.
Analysts say Maduro would be hard to beat given Chavez's personal blessing and the emotional outpouring from supporters if the president were forced to leave office, though past polls have shown Capriles to be more popular than the vice president.
Foreign investors generally hope for a more business-friendly government in Venezuela so prices of its widely traded bonds have soared over the last few weeks on Chavez's health woes, but they dipped this week as investors' expectations of a quick change apparently dimmed.