Ending one of Latin America's most remarkable populist rules, Mr Chavez died late on Tuesday at 58 after a two-year battle with cancer that was first detected in his pelvis.
Thousands of Venezuelans took to the streets to honour the flamboyant and outspoken leader whose body was taken to a military academy to lie in state for three days.
The government has declared seven days of mourning.
The future of Mr Chavez's leftist policies, which won him the adoration of poor Venezuelans but infuriated opponents who denounced him as a dictator, now rests on the shoulders of Vice-President Nicolas Maduro, the man he tipped to succeed him.
Mr Maduro said: "In the immense pain of this historic tragedy that has affected our fatherland, we call on all the compatriots to be vigilant for peace, love, respect and tranquillity.
"We ask our people to channel this pain into peace."
Mr Maduro, a 50-year-old former bus driver and union leader, will probably face opposition from Henrique Capriles, governor of Miranda state, in the next election in the Organisation of the Petroleum Exporting Countries nation with the world's largest oil reserves.
The stakes are huge for the region, given the Chavez government's crucial economic aid and cheap fuel supplies to allies across Latin America and the Caribbean.
Authorities said the vote would be called within 30 days, but it was not clear if that meant it would be held, or simply the date would be announced.
A victory by Mr Capriles, 40, a centrist politician who calls Brazil his model for Venezuela, would bring big changes and be welcomed by business groups, although he would probably move cautiously to lower the risk of political instability.
Mr Capriles called for unity and respect for the loss that many felt after Mr Chavez's demise.
He said: "This is not the time to stress what separates us.
"There are thousands, maybe millions, of Venezuelans asking what will happen, who even feel fear. Between us all, we're going to guarantee the peace this beloved country deserves."
Devastated supporters spoke out in tribute to Mr Chavez. In the city's central Plaza Bolivar, Nancy Jotiya, 56, said: "He was our father. He taught us to defend ourselves. Chavismo is not over. We are the people. We will fight."
There was sadness in other Latin American countries too, especially those run by leftist friends of Mr Chavez. Bolivian President Evo Morales flew in yesterday to join the mourning. The presidents of Argentina and Uruguay also arrived before dawn.
Messages of condolence flooded in – ranging from the secretary-general of the United Nations, Ban Ki-moon, to Chavez's ally Iran.
However, US President Barack Obama was less enthusiastic about a man who put his country at loggerheads with Washington, saying his administration was interested in "developing a constructive relationship with the Venezuelan government".
Mr Chavez led Venezuela for 14 years and had easily won a new six-year term at an election in October, defeating Mr Capriles.
His charisma, anti-US diatribes and oil-financed projects to improve life for residents of long-neglected slums created an unusually powerful bond with many poor Venezuelans.
That emotional connection underpinned his rule, but critics saw his autocratic style, nationalisations and often harsh treatment of rivals as hallmarks of a dictator whose policies squandered a bonanza of oil revenues.