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Chavez, 58, died after a long battle with cancer, plunging Venezuela into an uncertain future after 14 years of rule by the charismatic former paratrooper, a standard-bearer of Latin America's "anti-imperialist" left.
Brazilian President Dilma Rousseff hailed Chavez as a "great Latin American," describing his death as "an irreparable loss."
"We recognize a great leader, an irreparable loss and above all a friend of Brazil, a friend of the Brazilian people," she said before leading a minute of silence at a meeting with rural leaders in Brasilia.
Her predecessor, former president Luiz Inacio Lula da Silva, meanwhile expressed sadness over the death and recalled the Venezuelan leader's struggle for a "more just world."
Bolivia's socialist President Evo Morales -- whose political priorities and style of leadership have drawn deeply from his close ally Chavez -- said he was "crushed" by his friend's death and would soon travel to Venezuela.
"We are in pain. We are crushed," Morales said, before adding that the "liberation, not only of the Venezuelan people but also of Latin America's people broadly, must go on."
Ecuador's leftist President Rafael Correa, another close ally of Chavez, said his death was an "irreparable loss" for all of Latin America, saying Venezuelans would proudly carry on his legacy.
Communist Cuba, which depended economically on Chavez for years and was his main political ally in the region, broke into its regular television programming to announce his death.
Just moments after it opened, a percussion festival was called off as Havana started mourning Chavez, who had helped keep Cuba's crippled economy afloat by supplying it with cut-rate oil.
In Argentina, Vice President Amado Boudou said on Twitter that "all of Latin America" was in mourning.
"One of the best has left us: you will always be with us, Comandante," Boudou said.
Chilean President Sebastian Pinera, a conservative billionaire, called Chavez a leader who was "deeply committed to Latin America's integration." Chavez pushed to create the Community of Latin American and Caribbean States (CELAC).
As Latin American nations led the tributes, there was a more measured response from the United States, whom Chavez had delighted in antagonizing during his years in office.
"At this challenging time of President Hugo Chavez's passing, the United States reaffirms its support for the Venezuelan people and its interest in developing a constructive relationship with the Venezuelan government," President Barack Obama said.
"As Venezuela begins a new chapter in its history, the United States remains committed to policies that promote democratic principles, the rule of law, and respect for human rights," Obama said in a short written statement.
Canadian Prime Minister Stephen Harper meanwhile offered condolences to Venezuela while expressing hope of working with Chavez's successor to build a region which is "more prosperous, secure and democratic."
"At this key juncture I hope the people of Venezuela can now build for themselves a better, brighter future based on the principles of freedom, democracy, the rule of law and respect for human rights," Harper said.
In London, British Foreign Secretary William Hague said he was "saddened" by the death, saying the Venezuelan leader had left a "lasting impression" on his people.