The 58-year-old president won re-election in October and is due to be sworn in for a new six-year term on Jan. 10. If Chavez were to die, the constitution says that new elections should be called and held within 30 days.
Chavez said on Saturday that if such new elections are held, Maduro should be elected president in his place.
In the meantime, Maduro is helping to lead a government with serious economic problems including a swelling budget deficit and a currency that has a rapid drop in black market trading.
The vice president is also actively campaigning ahead of this weekend's state elections, telling supporters on Monday that when casting ballots "we're there with Chavez."
Chavez plans to undergo his third operation to remove cancerous tissue in about a year and a half. An initial surgery for a pelvic abscess in June 2011 helped reveal he had cancer. 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 on Nov. 27 returned to Cuba saying he would undergo hyperbaric oxygen treatment. Such treatment is regularly used to help heal tissues damaged by radiation treatment.
He said that while in Cuba tests found a return of "some malignant cells" in the same area where tumors were previously removed. Chavez said he will undergo surgery in the coming days, but it's not clear how soon.
As Chavez arrived in Havana in the early morning darkness, he received a typical welcome from Cuban President Raul Castro, who hugged him and smiled for the cameras.
But he also received a last-minute visit from Ecuadorean President Rafael Correa, who flew to Cuba on Monday.
"He has a very grave health problem," Correa told reporters at Havana's international airport. "We came to give him a hug in the name of the Ecuadorean people. ... He is not alone."
Associated Press writers Ian James in Caracas and Andrea Rodriguez in Havana contributed to this report.