Chavez was flanked by Maduro and Cabello, and he held a small blue copy of the constitution in his hands. Concluding his talk, Chavez called for his aides to bring out a sword that once belonged to Bolivar, and showed it to Maduro.
"Before that sword we swear... we will be paying close attention, and I ask for all the support, all the support of the nation," Chavez said.
State television showed Chavez's supporters congregating in city squares on Sunday and joining hands to pray for his health. In downtown Caracas, some expressed optimism that Chavez would pull through it. Others said they weren't sure.
"I love Chavez, and I'm worried," said Leonardo Chirinos, a construction worker. "We don't know what's going to happen, but I trust that the revolution is going to continue on, no matter what happens."
Chavez called his relapse a "new battle." It will be his third operation to remove cancerous tissue in about a year and a half.
The president underwent surgery for an unspecified type of pelvic cancer in Cuba in June 2011, after an earlier operation for a pelvic abscess. He had another cancer surgery last February after a tumor appeared in the same area. He has also undergone chemotherapy and radiation treatments.
Chavez said in July that tests showed he was cancer-free. But he had recently reduced his public appearances, and he made his most recent trip to Cuba on Nov. 27, saying he would receive hyperbaric oxygen treatment. Such treatment is regularly used to help heal tissues damaged by radiation treatment.
Chavez said that while in Cuba tests detected the recurrence of cancer.
Dr. Julian Molina, an oncologist at the Mayo Clinic in Rochester, Minnesota, said that based upon the limited information Chavez has made public about his cancer it appears to be terminal.
"For a patient in similar circumstances where you have given surgery as a first line of treatment, then chemotherapy, then radiation therapy and you are still dealing with a tumor this late — that indicates that it is not a curable cancer," he told The Associated Press in a telephone interview.
Molina and other medical experts said Chavez's next surgery likely won't be high-risk.
"I think if they are planning to do any surgery it is to improve his quality of life, meaning to remove a tumor that is located in a place that is either producing some pain or some difficulty for the patient," Molina said.
He agreed with other doctors queried by the AP that Chavez could have a sarcoma, which he said tend to spread to the lungs. Based on Chavez's treatment regimen, he said, it's highly unlikely he's suffering from colon or prostate cancer, though it could also be bladder cancer.
Molina said it is extremely difficult to say how long Chavez has to live. "You need to know more specifics about the case," he said.
Chavez said he wouldn't have run for re-election this year if tests at the time had shown signs of cancer. He also made his most specific comments yet about his movement carrying on without him if necessary.
"Fortunately, this revolution doesn't depend on one man," Chavez said. "Today we have a collective leadership."
Throughout his presidency, though, Chavez has been a one-man political phenomenon, and until the appointment of Maduro he hadn't designated any clear successor.
"Chavez is in the short term irreplaceable in terms of leadership and of national impact," said Luis Vicente Leon, a pollster who heads the Venezuelan firm Datanalisis.
Still, he said, Chavez's announcement could help his party's candidates rally support in upcoming state gubernatorial elections on Dec. 16. Leon also said that if Chavez's candidates have a strong showing, it could give his party an added boost to promote constitutional changes to allow Maduro to succeed Chavez without the need for a new election. Such a possibility has not been publicly raised by Chavez's political allies.
Opposition leader Henrique Capriles, who was defeated in the presidential vote, wished Chavez a speedy recovery.
He also bristled at the idea of Maduro being a designated political heir, saying: "When a person leaves his position the public has the last word, because we're in Venezuela and not Cuba."
"Here you can't talk about successors," Capriles said.
Associated Press writers Fabiola Sanchez and Christopher Toothaker in Caracas and Frank Bajak in Bogota, Colombia, contributed to this report.
Ian James on Twitter: http://twitter.com/ianjamesap