CARACAS, Venezuela (CNN) -- Venezuelans, by the slimmest of margins, rejected a constitutional referendum that would have allowed President Hugo Chavez to seek re-election indefinitely and tightened socialism's grip on the oil-rich Latin American nation.
By 51 percent to 49 percent, voters shot down a referendum that included 69 proposed amendments to the 1999 constitution, according to Monday reports from the National Electoral Council. In all, 9 million of Venezuela's 16 million eligible voters went to the polls.
"Don't feel sad. Don't feel burdened," Chavez told supporters after the results were announced.
In Washington, the White House applauded the vote.
"We congratulate the people of Venezuela on their vote and their continued desire to live in freedom and democracy," said National Security Council spokesman Gordon Johndroe.
Thousands of Venezuelans gathered in the streets of Caracas, many of them university students who worked to defeat the measure, and burst into singing their country's national anthem upon hearing the news.
One of the more controversial proposed amendments would have abolished term limits, allowing the firebrand Chavez to hold office indefinitely as long as he is re-elected.
The 53-year-old Venezuelan president was voted into power in 1998 and has twice been re-elected by large margins. The present law prohibits Chavez from seeking re-election when his term ends in 2012.
Another amendment on the ballot would have pushed the country more toward socialism. The leftist Chavez has said he should have full authority over the autonomous Central Bank as well as the nation's economic policy. These measures, Chavez has said, are necessary to move the economy toward socialism.
Since winning a second six-year term in December, Chavez has promised to push forward with his particular brand of socialism and his "Bolivarian Revolution."

Used oil to garner support

Chavez has used skyrocketing oil revenues, which reportedly account for about 90 percent of the nation's export earnings, to garner support in the country's poorer neighborhoods.
In Venezuela, the poor receive free health care and education, much like in Cuba, which is under the rule of Chavez's friend and mentor, President Fidel Castro.
In the last year, Chavez has nationalized oil, telephone and power companies and refused to renew the broadcast license for RCTV, an independent television station that had been broadcasting for 53 years.
The Venezuelan government later threatened to investigate broadcasters it said were inciting the public to violence over the decision. RCTV returned as a cable and satellite broadcaster in July.
On Friday, Chavez threatened to take independent Venezuelan network Globovision off the air if it broadcast partial results of the Sunday referendum.
Chavez, a former paratrooper, also routinely lambastes the United States, which has had thin diplomatic but close economic ties with Venezuela. The United States is Venezuela's top oil customer, buying about 1 million barrels a day, and is one of the few countries that can refine its low-quality crude.
Despite Sunday's defeat, Chavez -- in what he called a talk "from my heart" -- thanked those who opposed his proposals and said the election results proved Venezuelan democracy was maturing, a sentiment echoed by Tibisay Lucena, president of the National Electoral Council.