President Chavez has been in power for 10 years
The US has cautiously welcomed Venezuela's vote to scrap limits on how often politicians, including President Hugo Chavez, can run for office.
State Department spokesman Noel Clay praised "the civic spirit" of the referendum on Sunday.
But he said it was important that elected officials in Venezuela focused "on governing democratically".
Mr Chavez is one of Washington's most outspoken critics, who last year expelled the US ambassador in Caracas.
Mr Chavez has said he needs to stay in office beyond the end of his current term in 2012 so he can secure what he calls Venezuela's socialist revolution.
Critics say that would concentrate too much power in the presidency.
On Monday, Venezuela's electoral commission said that with 94% of votes counted, 54% backed an end to term limits.
"The doors of the future are wide open," Mr Chavez shouted from the balcony of the Miraflores presidential palace after the results were announced.
CHAVEZ DECADE: KEY DATES
Feb 1999: Takes office after winning 1998 election
July: Re-elected under new constitution for a six-year term
April 2002: Abortive coup. Chavez returns to power after two days
August 2004: Wins recall referendum on whether he should serve out rest of his term
Dec 2006: Wins another six-year term with 63%
Dec 2007: Loses constitutional referendum which included proposal to allow the president to run indefinitely for office
Feb 2009: Wins referendum that lifts term limits on elected officials
"In 2012 there will be presidential elections, and unless God decides otherwise, unless the people decide otherwise, this soldier is already a candidate."
Crowds of the president's supporters filled in the streets, letting off fireworks, waving red flags and honking car horns.
The BBC's Will Grant in the Venezuelan capital, Caracas, says this was the kind of strong confirmation of his socialist agenda at the polls that Mr Chavez had been seeking.
More than 11 million voters out of almost 17 million who were eligible took part in the referendum, said the head of the electoral body, Tibisay Lucena.
Election observers, who included representatives from Latin American nations, European Parliament deputies and European academics, said the ballot had been free and fair.
Opposition figures said they would not contest the result but they said victory had been achieved thanks to huge government funding and blanket state television coverage.
Under existing constitutional rules, the president was limited to two six-year terms in office, which meant that Mr Chavez would have had to leave the presidency in three years' time.
A proposal to end presidential term limits was one of a package of 69 constitutional changes narrowly rejected in a referendum in late 2007.