A close ally of Cuba's Fidel Castro, Chavez has redistributed more oil wealth than past Venezuelan leaders, and also has aided Latin American allies -- including Bolivia, Ecuador and Nicaragua -- that have followed Venezuela's turn to the left.
"He is a man who feels for the people, a man who has suffered, a man who comes from below," Carlos Orlando Vega, a 47-year-old carpenter's assistant, said outside a polling station in a Caracas slum on Sunday.
Vega is among tens of thousands of Venezuelans who, under Chavez, have new government-provided homes.
Chavez urged calm and restraint after his Sunday setback.
"I wouldn't have wanted that Pyrrhic victory," he said, suggesting a small margin wouldn't have been enough of a mandate.
Tensions surged in the weeks ahead of Sunday's vote, with university students leading protests and occasionally clashing with police and Chavista groups.
Chavez had warned opponents against inciting violence before the vote, and threatened to cut off oil exports to the United States if the Bush administration interfered.
Chavez, 53, also suffered some high-profile defections by political allies, including former defense minister Gen. Raul Baduel.
Early Monday, Baduel reminded fellow Venezuelans that Chavez still wields special decree powers thanks to a pliant National Assembly packed with his supporters.
"These results can't be recognized as a victory," Baduel told reporters,
Baduel, who as defense minister helped Chavez turn back the 2002 putsch, said Venezuela can only be properly united by convening a popularly elected assembly to rewrite its constitution.
Chavez has progressively steamrolled a fractured opposition since he was first elected in 1998, and his allies now control most elected posts.
At opposition headquarters in an affluent east Caracas district, jubilant Chavez foes sang the national anthem.
"This reform was about democracy or totalitarian socialism, and democracy won," said opposition leader Leopoldo Lopez said.
"At least now we have the guarantee that Chavez will leave power," said Valeria Aguirre, a 22-year-old student who had braved tear gas during street protests.
Lucena, the electoral agency chief, called the vote "the calmest we've had in the last 10 years."
All was reported calm during Sunday's voting but 45 people were detained, most for committing ballot-related crimes like "destroying electoral materials," said Gen. Jesus Gonzalez, chief of a military command overseeing security.