"This is not Cuba, nor is it a monarchy where a king designates the next king," the newspaper El Nacional quoted Henrique Capriles Radonski as saying Sunday. "The last word belongs to the people."
Capriles, 40, wished Chavez, 58, a long life and a complete recovery.
"May God bless him and the virgin cover him with her mantle," Capriles said at a campaign stop ahead of next week's gubernatorial election.
Capriles, the governor of Miranda, one of the country's most populous states, which includes part of Caracas, the capital, is running for re-election in a race The New York Times said was difficult.
Chavez was back in Cuba Monday for further cancer surgery after flying to Caracas from Havana to announce on national television Saturday night his cancer had returned. He flew back to Havana early Monday.
Chavez said somberly on television it was a possibility he might not be able to continue as president or begin his new term in office next month.
In that case, "my strong opinion, as clear as the full moon, irrevocable, absolute, total," is that "you should elect [Vice President] Nicolas Maduro" as the new president.
"I ask it from my heart," Chavez said with Maduro at his side and a bust of South American independence leader Simon Bolivar behind them.
He spoke several times of the importance of "unity" in Venezuela and said he hoped he would recover fully.
"With the grace of God, as on the previous occasions, we'll come out victorious," he said, holding up a crucifix and kissing it.
Chavez, president since Feb. 2, 1999, was elected to a fourth term in October, defeating Capriles 55 percent to 44 percent.
Capriles' portion of the popular vote was far more than any previous candidate against Chavez.
His new six-year presidential term begins Jan. 10.
But if Chavez dies or cannot continue to govern before then, the Chavez-influenced Constitution, adopted in 1999, says Maduro, as vice president, would become president and finish out the current term's remaining days.
It says if Chavez is able to begin his new term, or if he leaves office within the first four years, new elections would have to be called within 30 days.
"We don't know if Chavez is telling the truth about his health or if this is a political ploy," Maria Elena Ferrer, a Venezuelan national and political author who runs the Humanamente consulting firm in New York, told United Press International Sunday night.
"But if Chavez is telling the truth -- and therefore putting at risk all his party's gubernatorial candidates a week before Sunday's election -- then he must be very ill," she said.
"Because people don't vote for his United Socialist Party or for his revolution," she said. "They vote for Chavez. And if Chavez is out of the picture, everything gets very confused."
Notable deaths of 2014 [PHOTOS]