Throngs of shocked supporters gathered in squares across the South American country to pray for and show solidarity with the 58-year-old socialist leader, who was re-elected for a new six-year term in October.
In his first public acknowledgement that his illness could force him to step down, Chavez said his vice president and foreign minister, Nicolas Maduro, would take over if he is incapacitated, and urged supporters to vote for him if an election is held.
"With God's will, like on the previous occasions, we will come out victorious," Chavez said late on Saturday (local time) from the presidential palace alongside ashen-faced ministers.
His departure from office, either before or after the scheduled January 10 start of his new term, would trigger an election within 30 days. It would mark the end of an era for the Latin American left, depriving it of one of its most acerbic voices and Washington's loudest critic in the region.
A clutch of Latin American and Caribbean neighbours, from Cuba and Nicaragua to Bolivia and Ecuador, depend on Chavez's oil-financed generosity to bolster their fragile economies.
Cuba has been the biggest beneficiary with Chavez's government shipping about 115,000 barrels of oil per day to the communist-led island on preferential terms.
An unruly transition from Chavez's highly centralized rule also could raise the specter of political instability in Venezuela, which holds the world's largest crude oil reserves.
Allies lack Chavez's charisma and may struggle to control his unwieldy coalition of military and leftist leaders.
FORMER BUS DRIVER NAMED SUCCESSOR
Among them, though, Maduro - a 50-year-old, mustachioed former bus driver and union leader - is widely viewed as the most popular among Venezuelans, thanks to his affable manner, humble background and close relationship with Chavez.
While his humble roots appeal to the president's working class supporters, Maduro's six years as Chavez's foreign minister have boosted his profile with the leaders of China, Russia and other world powers.
He has an easygoing style but also is a firm believer in Chavez's socialist policies and has often led fierce criticism of the United States.
Speculation about Chavez's health had grown during a three-week absence from public view that culminated in his latest trip for medical tests in Cuba. He has undergone three cancer operations and had two tumors removed there since June 2011. He had twice claimed to be cured, only for the cancer to return.
Chavez arrived in Venezuela on Friday after the latest tests, and is due to have the operation in Cuba in the next few days. Venezuela's National Assembly held a special session on Sunday to approve his trip, a formality required whenever the president travels overseas for more than five days.
Chavez said he had rejected the advice of his medical team to have the surgery sooner, on Friday or this weekend, telling them he needed to fly back to Venezuela to seek that permission.
"I decided to come, making an additional effort, in truth, because the pain is not insignificant," Chavez said in his televised address, which was also shown live in Cuba.
His return to Cuba may mark the start of another lengthy period of silence from government officials, combined with furious rumors over what political changes might be in store and what Chavez's actual condition is.
He has never revealed what type of cancer he has, saying only that it was in the pelvic area. He said on Saturday that the latest recurrence was in the same region.
Opposition leaders wished Chavez well but criticized him for excessive secrecy and not using local healthcare.
"They said he was cured ... Venezuela has the right to know the truth," one leader, Julio Borges, told the assembly.
NEW PRESIDENTIAL VOTE?
Chavez has been receiving treatment at Havana's Cimeq hospital as a guest of his close friend and political mentor, former Cuban leader Fidel Castro. He is guaranteed tight security and privacy on the communist-led Caribbean island.
The usually loquacious Venezuelan leader had sharply cut back appearances since winning the Oct. 7 election, saying the campaign and radiation therapy had left him exhausted.
Venezuela's constitution stipulates a new election if Chavez leaves office, unless it is in the last two years of his six-year term, when his vice president would take over.
Publicly naming long-time ally Maduro was a surprise.
"He is a complete revolutionary, a man of great experience despite his youth, with great dedication and capacity for work," Chavez said.
Maduro may win less support from the military wing of the Socialist Party, which controls many top government posts. His naming sidelines Diosdado Cabello, who heads Congress and is a former army comrade of Chavez. Perhaps fearing in-fighting, Chavez urged unity again and again in his comments.
"I never argue with Chavez's instructions, I obey them," Cabello told state TV afterward. "I am at the service of the vice president, at the service of the fatherland."
If a new election were needed, the opposition could be in its best position to win since Chavez took power in 1999. Many voters have ignored the failings of Chavez's government because of their intense emotional connection to him.
Henrique Capriles, a state governor, lost to Chavez in the October election, winning 44 percent support and a record 6.5 million votes for the opposition. He has broad support in opposition ranks and could run for president again.
Although past polls have shown Capriles is more popular than any of Chavez's allies - including Maduro - the vice president will benefit from his boss's personal blessing.
Venezuela's widely traded bonds are likely to soar when markets open on Monday on bets that Chavez's renewed illness will lead to a more market-friendly government.
Chavez's cancer saga has once again distracted attention from major national issues like state elections in a week, a possible devaluation of the bolivar currency, and a proposed amnesty for jailed and exiled political foes.