"We have been informed of new complications that arose as a consequence of the respiratory infection we already knew about," Nicolas Maduro said in a solemn broadcast from Havana, without saying what medical issues had arisen.
He spoke in the Sunday night broadcast from behind a table next to the Venezuelan flag, flanked by his wife, Attorney General Cilia Flores; Chavez's daughter, Rosa Virginia; and her husband, Science Minister Jorge Arreaza.
Maduro, 50, said the four had just visited the 58-year-old Chavez, who "greeted us and he himself talked about these complications," which follow excessive bleeding after a 6-hour operation Dec. 11 -- his fourth -- for an undisclosed type of cancer in his pelvic area.
A respiratory infection followed a week later, the government said.
"The state of health of President Chavez continues to be delicate," Maduro said, adding he would remain in Havana "for the coming hours" without saying how long.
He arrived in Havana Saturday.
Later Sunday, Venezuelan Information Minister Ernesto Villegas said a government-organized New Year's Eve concert in Caracas, the capital, had been canceled and he urged Venezuelans to pray for Chavez's recovery.
The government first announced Chavez's cancer in June 2011.
Chavez, in power since 1999, won re-election Oct. 7, defeating Henrique Capriles, the governor of Miranda, one of the country's most populous states, which includes part of Caracas.
Chavez is scheduled to be inaugurated for his third term Jan. 10.
National Assembly Speaker Diosdado Cabello has said the swearing-in ceremony would be postponed if Chavez can't make it, the BBC reported Monday.
But opposition leaders say postponing the inauguration would be unconstitutional, the network said.
Government officials say the Constitution makes no provision for what happens if a president-elect cannot take office on inauguration day.
The Constitution does say that in the case of an "absolute absence" of the president, elections must be held within 30 days.
Chavez said Dec. 9 that if his health fails, Venezuelans should vote for Maduro.
Capriles responded: "This is not Cuba, nor is it a monarchy where a king designates the next king. The last word belongs to the people."