Before flying to Cuba, Maduro said that Energy Minister Hector Navarro would be in charge of government affairs in the meantime.
"The situation does not look good. The fact that Maduro himself would go to Cuba, leaving Hector Navarro in charge only seems understandable if Chavez's health is precarious," said David Smilde, a University of Georgia sociologist and analyst for the Washington Office on Latin America think tank.
Smilde said that Maduro probably made the trip "to be able to talk to Chavez himself and perhaps to talk to the Castros and other Cuban advisers about how to navigate the possibility of Chavez not being able to be sworn in on Jan. 10."
"Mentioning twice in his nationally televised speech that Chavez has suffered new complications only reinforces the appearance that the situation is serious," Smilde said.
Medical experts say that it's common for patients who have undergone major surgeries to suffer respiratory infections and that how a patient fares can vary widely from a quick recovery in a couple of days to a fight for life on a respirator.
Maduro's latest update differed markedly from a week ago, when he had said he received a phone call from the president and that Chavez was up and walking.
The vice president spoke on Sunday below a picture of 19th century independence hero Simon Bolivar, the inspiration of Chavez's leftist Bolivarian Revolution movement.
Maduro said that Chavez had sent year-end greetings to his homeland and a "warm hug to the boys and girls of Venezuela."
The vice president expressed faith that Chavez would "successfully fight this new battle." He concluded his message saying: "Long live Chavez."
On the streets of Caracas, images of Chavez smiling and saluting are emblazoned on campaign signs and murals. One newly painted mural reads: "Be strong, Chavez."
State television played video of Chavez campaigning for re-election, including a speech when he shouted: "I am a nation!"
A new government sign atop a high-rise apartment complex reads: "YOU ALSO ARE CHAVEZ."
Chavez has been in office since 1999 and was re-elected in October, three months after he had announced that his latest tests showed he was cancer-free.
Opposition politicians have criticized a lack of detailed information about Chavez's condition, and last week repeated their demands for a full medical report.
Information Minister Ernesto Villegas defended the government's handling of the situation, saying during a televised panel discussion on Sunday night that Chavez "has told the truth in his worst moments" throughout his presidency.
He also referred to a new surge of rumors about Chavez's condition and called for respect for the president and his family.
Chavez's daughter Maria, who has been with the president since his surgery, said in a message on her Twitter account: "Thank you people of Venezuela. Thank you people of the world. You and your love have always been our greatest strength! God is with us! We love you!"
Chavez's son-in-law Jorge Arreaza, who is the government's science minister and has been with the president in Cuba, urged Venezuelans in a Twitter message Monday night not to believe "bad-intentioned rumors" circulating online. "President Chavez has spent the day calm and stable, accompanied by his children," Arreaza said in the message.
Some who stood in the Caracas plaza on Monday night held pictures of the president. Speaking to the crowd, lawmaker Earle Herrera said that Chavez "is continuing to fight the battle he has to fight."
"He's an undefeated president, and he'll continue to be undefeated," he said.
Associated Press writer Christopher Toothaker contributed to this report.
Ian James on Twitter: http://twitter.com/ianjamesap