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