Venezuelan Vice President Nicolas Maduro announced that Chavez, 58, died Tuesday after a long bout with cancer.
European Commission President Jose Manuel Barroso relayed condolences in a personal message to Maduro.
"Venezuela has stood out for its social development and for its contribution to South America's regional integration," the message said. "Hoping to deepen our relationship in the future, we would like to send our sincere condolences and sympathy to the people and the government of Venezuela."
Social programs helped earn Chavez a reputation as a hero for the country's poor. His efforts at nationalization, however, brought opposition from middle and upper classes.
The World Bank states that Venezuela's gross domestic product grew 4.2 percent in 2011, up from an 8.9 percent contraction reported nearly 10 years ago.
Chavez ally, Iranian President Mahmoud Ahmadinejad, said the death of the Venezuelan president was a great loss to the country.
"Indeed, he is a martyr (who lost his life) in the path of serving the Venezuelan people and preserving human and revolutionary values," Ahmadinejad was quoted by Iran's Press TV as saying.
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