The vote was reported to have been extremely close, with earlier electoral authority reports putting the figures at 49.2% to 50.7% against Chavez.
Chavez had claimed that the changes would return power to the Venezuelan people. His opponents, however, accused him of a power grab.
"We will accept the results whatever they are. Venezuelans have never voted so often as during these nine years of peaceful and democratic revolution," Chavez said after casting his vote on Sunday.
Turnout was reported to have been high, and long queues were reported at polling stations across the country. The referendum also sought to reduce the minimum voting age from 18 to 16.
Under the current Venezuelan Constitution, Chavez is due to stand down as president when his term expires at the end of 2012.