The White House has said it welcomes the defeat of Venezuelan President Hugo Chavez's controversial reform plans in a referendum.
The president said his battle for "socialism" would go on
"It looks like the people spoke their minds... and I think that bodes well for the country's future and freedom and liberty," a spokeswoman said.
Mr Chavez narrowly lost his bid to change the constitution but says he will try again to win approval.
The changes would let a president stand indefinitely for re-election.
They were defeated by 51% of the vote to 49%, officials said.
Accepting the result, which came as a wide surprise not only to his supporters but also to his opponents, Mr Chavez urged his followers to remain calm.
But it was his first electoral defeat since he came to power in 1998 and is being seen as a major blow to his plan to make Venezuela a socialist republic, BBC Americas reporter Julian Miglierini reports.
Still in power
Many point to the levels of abstention registered at Sunday's election as an explanation for the defeat: more than 40% of Venezuelans did not vote.
It is thought that the bulk of those who abstained were made up of Chavez supporters who chose not to endorse the reforms proposed by their leader.
Apart from ending limits on presidential terms, the reforms would have halted the central bank's autonomy and cut the working week.
It is believed that opponents to Mr Chavez turned out massively at polling stations after a campaign led by students, who have become the most prominent voices of Venezuelan opposition.
The defeat, however, does not mean that Mr Chavez is losing his strong grip on power, our Americas reporter adds.
The president still dominates the country's congress, a law passed in January allows him to govern by decree and his current presidential mandate lasts until 2013.
Opposition celebrations began almost immediately after the result was known in the capital, Caracas.
Indefinite re-election of president, term increased from 6 to 7 years
Central Bank autonomy ended
Structure of country's administrative districts reorganised
Maximum working day cut from 8 hours to 6
Voting age lowered from 18 to 16
Social security benefits extended to workers in informal sector
"Venezuela won today, democracy won today, and I am sure that this victory for the Venezuelan people will have a very important impact in the rest of Latin America," Leopoldo Lopez, opposition mayor of the Chacao of Caracas municipality, told the BBC.
In a statement from the White House, the US state department said the Venezuelan people had delivered a clear message that they did "not want any further erosion in their democracy and their democratic institutions".
Mr Chavez congratulated the opposition but asked them to "go home [and] know how to handle [their] victory".
He insisted that he would "continue in the battle to build socialism" and that his reforms proposal was "still alive".
Since winning power in 1998, Mr Chavez has set about introducing sweeping changes in the country's laws aimed at redistributing Venezuela's oil wealth to poorer farmers in rural areas.
Just a year ago, he was re-elected with 63% of the vote.