Venezuelanalysis.com reported the 58-year-old socialist announced on public television that malignant cells have returned to the area of his body that previously had been affected. He said he will transfer his presidential powers to Vice President Nicolas Maduro during his absence.
Noting "there are always risks in processes like this," Chavez, who is to begin a new six-year term in January, said "if anything happens to me that hinders me," he wants Maduro to replace him, Venezuelanalysis.com said.
"My strong opinion, as clear as the full moon, irrevocable, absolute, total," Chavez said, is that Maduro should succeed him if he is unable to resume his duties, The New York Times quoted him as saying.
"I ask it from my heart," he said.
The Times reported Chavez appeared reserved during his address from the presidential palace. Maduro sat to his left and several Cabinet members also were on hand, the newspaper said.
Chavez said that he would fly to Havana Sunday for the operation, the Times said.
He said tests immediately after his re-election showed no malignancy but he subsequently experienced pain and swelling that prompted him to return to Cuba Nov. 27 for further tests.
Chavez was first diagnosed with cancer in June 2011. He has undergone surgery, chemotherapy and radiation treatment but has never disclosed what type of cancer he has.
MercoPress reported Chavez had appeared in good spirits upon his return to Caracas Friday.
"I'm happy and enthused to be back again," Chavez said.
"So, where's the party?"