Chávez, who won re-election on October 7, also said for the first time that if his health were to worsen, his successor would be Vice President Nicolas Maduro.
"We should guarantee the advance of the Bolivarian Revolution," Chávez said on television, seated at the presidential palace with Maduro and other aides.
Outside medical experts said that based on Chávez's account of his condition, he is facing a very difficult fight against cancer.
The president, who just returned from Cuba early on Friday, said tests had shown a return of "some malignant cells" in the same area where tumors were previously removed.
"I need to return to Havana tomorrow," Chávez said, adding that he would undergo surgery in the coming days.
Chávez's quick trip home appeared to allow him to send a clear directive to his inner circle that Maduro would be his chosen successor. He called for his allies to pull together, saying: "Unity, unity, unity."
Chávez named Maduro, his longtime foreign minister, as his choice for vice president three days after winning re-election. Maduro, a burly former bus driver, has shown unflagging loyalty and become a leading spokesman for Venezuela's socialist leader in recent years.
The vice president's expression was solemn as Chávez said that Maduro should become president if any complication were to prevent him from finishing his current term, which concludes in early January. Chávez said that if new elections are held, his movement's candidate should be Maduro.
"You all elect Nicolas Maduro as president," Chávez said, holding a small blue copy of the Constitution in his hands and waving it.
The Venezuelan Constitution says that if a president-elect dies before taking office, a new election should be held within 30 days and that in the meantime the president of the National Assembly is to be in charge of the government.
While he spoke, Chávez was seated at a table flanked by both Maduro and national assembly president Diosdado Cabello.
Chávez is scheduled to be sworn in for a new six-year term on January 10, and he called his relapse a "new battle".
He is to undergo his third operation to remove cancerous tissue in about a year and a half.
The 58-year-old president first underwent cancer surgery for an unspecified type of pelvic cancer in Cuba in June 2011, after an operation for a pelvic abscess earlier in the month found the cancer. He had another cancer surgery last February after a tumor appeared in the same area. He has also undergone chemotherapy and radiation treatments.
Chávez said tests immediately after his re-election win had shown no sign of cancer. But he said he had swelling and pain, which he thought was due to "the effort of the campaign and the radiation therapy treatment".
"It's a very sensitive area, so we started to pay a lot of attention to that," he said, adding that he had reduced his public appearances.
Chávez made his most recent trip to Cuba on the night of November 27, saying he would receive hyperbaric oxygen treatment. Such treatment is regularly used to help heal tissues damaged by radiation treatment.
Chávez said that he has been coping with pain and that while he was in Cuba thorough exams detected the recurrence of cancer.
He arrived back in Caracas on Friday after 10 days of medical treatment in Cuba, but until Saturday night had not referred to his health. His unexplained decision to skip a summit of regional leaders in Brazil on Friday had raised suspicions among many Venezuelans that his health had taken a turn for the worse.
Chávez said that he was requesting permission from lawmakers to travel to Havana.
"I hope to give you all good news in the coming days," said Chávez, who held up a crucifix and kissed it. "With the grace of God, we'll come out victorious."
Dr Carlos Castro, scientific director of the League Against Cancer in neighbouring Colombia, told the Associated Press that he expects the operation will likely be followed by more chemotherapy.
"It's behaving like a sarcoma, and sarcoma doesn't forgive," Castro said, adding that he wouldn't be surprised if the cancer had also spread to the lungs or other areas.
"We knew this was going to happen," he said. "This isn't good."
Throughout his treatment, Chávez has kept secret various details about his illness, including the precise location of the tumours and the type of cancer. He has said he travels to Cuba for treatment because his cancer was diagnosed by doctors there.
Dr Michael Pishvaian, an oncologist at Georgetown University's Lombardi Cancer Centre in Washington, said in a phone interview that he wasn't surprised by the news.
"I think this is recurrent cancer that at this point is almost certainly not going to go away," Pishvaian said. "It's unlikely that what he's going through now is curable."
He speculated that given what Chávez has said about his cancer, it is most likely a soft-tissue sarcoma. He said those in the pelvis area have a likelihood of recurring of 50 to 70%, even with the best treatment. – AP