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 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 centralised 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. 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 tumours 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 rumours over what political changes might be in store and what Chavez's actual condition is.