Henrique Capriles, 40, said there were more than 300,000 incidents from Sunday’s poll that needed to be examined.
However, the electoral authorities said Socialist Nicolas Maduro would be confirmed as the winner.
Nicolas Maduro has called for the results to be respected.
The National Electoral Council is due to formally proclaim Nicolas Maduro’s victory at a ceremony and rally in Caracas later on Monday.
The election was called after Hugo Chavez’s death from cancer last month.
Nicolas Maduro, a former bus driver whom Hugo Chavez had named as his preferred heir, won 50.7% of the vote against 49.1% for Henrique Capriles.
The National Electoral Council said the results, which it announced on Sunday night, were “irreversible”.
Russian President Vladimir Putin and Cuban leader Raul Castro were among the first heads of state to congratulate Nicolas Maduro on his win.
Meanwhile the US has called for an audit of the results.
“This appears an important, prudent and necessary step to ensure that all Venezuelans have confidence in these results,” a White House spokesman said.
As the news of Nicolas Maduro’s victory emerged, celebrations erupted in the capital, Caracas.
Thousands of jubilant supporters took to the streets, dancing, singing and blasting car horns, while fireworks lit up the night sky. Opposition voters banged pots and pans in protest.
Speaking outside the presidential palace, Nicolas Maduro told crowds that the result was “just, legal and constitutional”.
He said his election showed Hugo Chavez “continues to be invincible, that he continues to win battles”.
Nicolas Maduro, who was wearing a tracksuit top in the colors of the Venezuelan flag, said he had spoken to Henrique Capriles on the phone, and that he would allow an audit of the election result.
He called for those who had not voted for him to “work together” for the country.
Nicolas Maduro’s margin of victory was far narrower than that achieved by Chavez at elections last October, when he beat Henrique Capriles by more than 10 percentage points.
Almost immediately, one member of the National Electoral Council who does not have government sympathies called on the authorities to carry out a recount by hand, a call later echoed by Henrique Capriles himself.
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