"I must complete this new step," Chavez said in Caracas before his departure, according to an AFP journalist. "I am going for a few days but I am not saying goodbye... I will return better," said Chavez who arrived in Cuba yesterday.
"It is not time for dying; it's time to live," he stressed.
The 56-year-old president gave a televised speech shortly before leaving Caracas, saying, "I have to say I am optimistic. I have never loved life the way I am loving it now."
He said that since the removal of a tumour "right up to this very day, no other cancerous cell has been detected in my body." It was a rare disclosure on an illness his critics complained the president kept too close to the vest.
Chavez, who was being accompanied by his daughter Rosa, was given a sendoff at the airport by most of his state ministers, for his stay in Cuba, the length of which is not known.
On Friday, Chavez asked the National Assembly for permission to travel to Cuba so he can continue treatment after his June 20 operation in Havana.
"I will travel to Havana to begin what we have called the second stage of this slow and complex process of recovery, which is going well," Chavez said on Friday.
Though the National Assembly unanimously approved his travel request, which is needed for the president to leave the country for more than five days, opposition leaders say it is unconstitutional for Chavez to continue to exercise executive authority from Cuba.
"When the president leaves the country, the vice president must assume the chief executive role. It is their duty," said opposition lawmaker Hiram Gaviria.
"The health of the country must be put above the president's health. We must be serious. We believe he should not hold office from Havana," added another opposition lawmaker, Carlos Berrizbeitia.
But other lawmakers say Chavez should continue his chief executive role, because he has the mental and physical capabilities to do so.
The president said he would hand over his full presidential powers to Vice President Elias Jaua only "if I felt my abilities were impaired." Chavez did issue a decree giving Jaua and Finance Minister Jorge Giordani a few administrative and economic powers.
Chavez, in power since 1999, is his party's candidate for the 2012 presidential election, where he will be seeking a third six-year term in office. His supporters accused political foes of encouraging a coup yesterday.
Critics of the president have demanded details of his cancer as well as answers to why he cannot be treated in Venezuela, where authorities say they have created a quality health care system.
The Venezuelan government has not explained the extent of Chavez's cancer or provided any other details about the disease.
Cuba, the America's only one-party communist regime, is Chavez's closest regional ally.