Before his operation, Chavez acknowledged he faced risks and designated Maduro as his successor, telling supporters they should vote for the vice president if a new presidential election were necessary.
Chavez said at the time that his cancer had come back despite previous surgeries, chemotherapy and radiation treatment. He has been fighting an undisclosed type of pelvic cancer since June 2011.
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 last Monday, 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 expressed faith that Chavez's "immense will to live and the care of the best medical specialists will help our president successfully fight this new battle." He concluded his message saying: "Long live 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.
Villegas said a government-organized New Year's Eve concert in a downtown Caracas plaza had been canceled, and he urged Venezuelans to pray for Chavez.
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!"
Allies of the president also responded on Twitter, repeating the phrase: "Chavez lives and will triumph."
Ian James on Twitter: http://twitter.com/ianjamesap