"It was a complex, difficult, delicate operation," Maduro said. "The post-operative process is also going to be a complex and hard process."
Without giving details, Maduro reiterated Chavez's recent remarks that the surgery presented risks and that people should be prepared for any "difficult scenarios."
The constitution says presidents should be sworn in before the National Assembly, and if that's not possible then before the Supreme Court.
Former Supreme Court magistrate Roman Duque Corredor said a president cannot delegate the swearing-in to anyone else and cannot take the oath of office outside Venezuela. A president could still be sworn in even if temporarily incapacitated, but would need to be conscious and in Venezuela, Duque told The Associated Press.
If a president-elect is declared incapacitated by lawmakers and is unable to be sworn in, the National Assembly president would temporarily take charge of the government and a new presidential vote must be held within 30 days, Duque said.
Chavez said Saturday that if an election had to be held, Maduro should be elected president.
The dramatic events of this week, with Chavez suddenly taking a turn for the worse, had some Venezuelans wondering whether they were being told the truth because just a few months ago the president was running for his fourth presidential term and had said he was free of cancer.
Lawyer Maria Alicia Altuve, who was out in bustling crowds in a shopping district of downtown Caracas, said it seemed odd how Maduro wept at a political rally while talking about Chavez.
"He cries on television to set up a drama, so that people go vote for poor Chavez," Altuve said. "So we don't know if this illness is for that, or if it's that this man is truly sick."
Some Chavez supporters said they found it hard to think about losing the president and worried about the future. His admirers held prayer vigils in Caracas and other cities this week, holding pictures and singing hymns.
Chavez has undergone four cancer-related surgeries since June 2011. He has also undergone months of chemotherapy and radiation treatments. Throughout his treatments, Chavez has kept secret some details of his illness, including the exact location and type of the tumors.
Ecuadorean President Rafael Correa wished his close ally the best, while also acknowledging the possibility that cancer might end his presidency. "Chavez is very important for Latin America, but if he can't continue at the head of Venezuela, the processes of change have to continue," Correa said at a news conference in Quito.
Associated Press writer Christopher Toothaker contributed to this report.