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CARACAS, Venezuela (CNN) -- Venezuelan President Hugo Chavez's detractors danced in the streets Monday after voters shot down a referendum that would have allowed the firebrand leftist to seek re-election indefinitely and tightened socialism's grip on his oil-rich nation.

In Caracas, Valencia, Maracaibo and other major cities, large crowds spilled into the streets, shouting, chanting, clapping and waving flags. One man carried a sign proclaiming, "Vota No," which by Monday was more an exclamation than an imperative after voters the day before dismissed 69 proposed amendments to Venezuela's 1999 constitution.

Chavez said Monday he accepted the vote, calling the slim margin of victory -- 51 percent to 49 percent, according to early reports -- a "photo finish."

The vote represented a rare poll defeat for Chavez, who has generally enjoyed popular support among the lower classes. Among the exceptions: a bitter national strike, an abortive coup against him in 2002 and a 2004 attempt to recall him as president, a vote he easily survived.

Many of Monday's revelers were university students who had worked doggedly to defeat the proposals. They burst into singing the national anthem upon hearing news that their efforts paid off.

"This is not a moment only for students; it is for the whole country," student Juan Andres Mejia said. "It's time for us to start walking the same path to walking together, and I think this day could be the start of a new republic of a new Venezuela."

In Washington, the White House applauded the results of 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.

In what he called a talk "from my heart," Chavez said the election results proved Venezuelan democracy was maturing, a sentiment echoed by Tibisay Lucena, president of the National Electoral Council.

Thanking his opponents, Chavez told a roomful of supporters and journalists, "Now Venezuelans should have faith in our institutions."

However, Chavez promised to continue his pursuit of the defeated proposals.

"Not a single comma of this proposal will be withdrawn," he said, holding up a small red book containing the text of the proposed changes. "I will continue proposing this to the Venezuelan people. The proposal is alive, not dead."

One of the more controversial proposed amendments would have abolished term limits, allowing Chavez to hold office indefinitely as long as he is re-elected.

The 53-year-old Venezuelan president, who was elected in 1998 as the country's youngest-ever president, has twice been re-elected by large margins. However, 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. 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."

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.

Chavez's opponents say he has undercut Venezuela's democracy by systematically concentrating power in his own hands.

In the last year, Chavez has nationalized oil, telephone and power companies and refused to renew the broadcast license for RCTV, an independent open-air 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.