the socialist leader shouted: "Chavez lives forever!" and "The fight continues!"
"We have to show that what he did was not in vain," said Jamila Rivas, 49, crying outside the military hospital where Chavez died. Hundreds of supporters flocked there.
Venezuelans have been tracking the ups-and-downs of Chavez's two-year battle against cancer, but some supporters felt a sense of disbelief that the flamboyant leader was gone.
"He was our father. 'Chavismo' will not end. We are his people. We will continue to fight!" said Nancy Jotiya, 56, in Caracas' downtown Bolivar Square, named for Venezuela's independence hero and Chavez's idol, Simon Bolivar.
"I admired him. He was a great man," said housewife Aleida Rodriguez, 50, who heard the news as she emerged from Caracas' underground transport system.
Venezuela's opposition leader, Henrique Capriles, offered condolences and called for unity.
Some opponents could not hide their happiness at the end to a rule they viewed as a cruel dictatorship.
"At last!" shouted some women, coming out of their homes in one upscale neighborhood.
Hatred for Chavez ran deep among the wealthier members of Venezuela's population.
Some openly celebrated his death on Twitter.
There were reports of isolated incidents of looting and violence, including the burning of tents belonging to students who had been protesting in a Caracas street for the last week against secrecy over Chavez's condition.
Around Latin America and the Caribbean, where Chavez's oil-fueled largesse was a source of support for various leftist governments, tributes and condolences poured in.
Bolivian President Evo Morales, a close personal friend, wept as he spoke of Chavez.
Brazil's Congress held a minute of silence.
"President Chavez has always been a friend of Brazil, regardless of his political position," said Renan Calheiros, president of the Brazilian Senate.
Colombia, whose pro-US conservative governments have clashed fiercely with Chavez in the past, also paid homage.
"I think in the last two years ... our relations with Venezuela advanced really well, and he was also a very important support for the current peace process," foreign minister Maria Angela Holguin said, referring to her government's rapprochement with Chavez and ongoing peace talks with leftist rebels.
"Hopefully he'll find peace."
Former Canadian prime minister Jean Chretien told CBC television he met Chavez several times, was quite fond of him, and acted as a facilitator between Chavez and former US President George W Bush at a 2001 Summit of the Americas.
"He was a great baseball fan and player and he always told me that if I were to visit him in Venezuela we would go to a baseball field and he would throw balls to me for me to hit them," he said. "And we never had the occasion to do that."