Government supporters, who gathered waiting to hear Chavez speak, vowed to win approval of reforms that would do away with term limits and expand Chavez's powers to remake the government and economy.
"Chavez has become a father for us," said Xiomi Diaz, 34, a farmer. "He's a father of the poor." She and others traveled from across the country in hundreds of buses.
The pro-Chavez rally came a day after more than 100,000 opposition supporters filled the same avenue promising to defeat revisions that would also extend presidential terms from six to seven years and create new forms of communal property.
Chavez denies he is trying to amass power, saying the changes are necessary to give the people a greater voice in government and to move toward a socialist system.
Human Rights Watch warned the changes would threaten fundamental rights, citing one that would allow the president to declare indefinite states of emergency during which the government could detain citizens without charge and censor the media.
"These amendments would enable President Chavez to suspend basic rights indefinitely by maintaining a perpetual state of emergency," Jose Miguel Vivanco of the New York-based group said in a statement Thursday.
In Washington, State Department spokesman Sean McCormack told reporters that the United States hopes that "the results of the referendum truly reflect the will of the Venezuelan people."
"It should be a free and fair contest in which the will and desire of the Venezuelan people is reflected," McCormack said.
Chavez's opponents have questioned the National Electoral Council's impartiality, especially after Chavez named its former chief, Jorge Rodriguez, as his own vice president in January. But in contrast to past elections, when the opposition has boycotted votes or been split on whether to participate, this time many opposition leaders are emboldened and urging voters to turn out in large numbers.
The government and the opposition both cite polls suggesting their side is ahead, raising tensions ahead of the referendum.
About 100 electoral observers from 39 countries in Latin America, Europe and the United States are on hand, plus hundreds of Venezuelan observers, the National Electoral Council said.
Yet absent this time are the Organization of American States and the European Union, which have closely monitored past votes. The short notice before the vote - on reforms approved by the solidly pro-Chavez National Assembly just one month before - has prevented both institutions from sending delegations that normally take six months to prepare.
The observers from the United States include delegations from the National Lawyers Guild and the National Association for the Advancement of Colored People.
Associated Press writer Fabiola Sanchez contributed to this report.
By Edison Lopez