Falcon, a loyalist of the late leftist firebrand Hugo Chavez who was neck-and-neck with Maduro in pre-election surveys
Venezuela was facing the threat of fresh international sanctions and intensified domestic unrest on Monday following President Nicolas Maduro's re-election in a vote rejected by the opposition as a farce.
Election officials said Maduro won 68% of the votes cast in Sunday's presidential poll, far ahead of the 21% won by his nearest rival, ex-army officer Henri Falcon.
In an address to cheering supporters outside Miraflores Palace in Caracas, Maduro hailed his victory for another six-year term as a "historic record."
"We won again! We triumphed again! We are the force of history turned into a permanent popular victory!" Maduro told those gathered to celebrate his "knockout" victory.
But the vote was marred by a 52% abstention rate - a historic high - following a boycott called by the Democratic Unity Roundtable (MUD) opposition coalition, which slammed the ballot as a "farce."
And even before it took place, the United States, Canada, the European Union and a dozen Latin American countries said they would not recognize the results.
Falcon, a loyalist of the late leftist firebrand Hugo Chavez who was neck-and-neck with Maduro in pre-election surveys, said the vote lacked "legitimacy" and accused the government of vote buying.
"For us, there were no elections," he told reporters. "We have to have new elections in Venezuela."
And third-placed Javier Bertucci, an evangelist preacher who polled around 11%, also joined the call for new elections.
Maduro may have won, but the near future appears bleak.
Venezuela is isolated and deep in the worst economic crisis of its history, with its people enduring food and medicine shortages, and a mass exodus of hundreds of thousands simply leaving the country.
The IMF estimates that Venezuela's GDP will continue to shrink this year, with the inflation rate expected to reach 13,800%.
Venezuela has always relied on its oil, but global prices are low and production has dropped to its lowest level in 30 years.
"The upcoming scenario is clear: political tension and radicalization, repression, massive international rejection, a sharpening of sanctions, and a climax to the economic crisis," said analyst Luis Vicente Leon.
Maduro, a former bus driver, union leader, foreign minister and Chavez's hand-picked political heir, has presided over an implosion of the once-wealthy oil producer's economy since taking office in 2013.
The socialist leader says Venezuela is the victim of an "economic war" waged by the conservative opposition and external powers including the United States aimed at toppling him.
Critics however blame him for gross economic mismanagement.
In his victory speech, Maduro acknowledged that "changes" were necessary.
"I will dedicate myself entirely towards economic recovery," he said, but gave few details.