Early Monday, National Electoral Council Director Vicente Diaz said the recount demanded by Capriles' opposition supporters would be granted.
"Given the close electoral result and the fact that we live in a polarized country, I would like to request that 100 percent of the ballot boxes be audited," he said.
Maduro, the acting president who was Chavez's handpicked heir, won by about 1.7 percent, with about 7.5 million votes, or 50.66 percent, compared with about7.3 million votes, or 49.1 percent, for Capriles, the National Electoral Council announced late Sunday after declaring more than 99 percent of the votes counted.
The percentage separating the two amounted to about 234,000 votes, the council said. The country's population is 29 million.
The council said the voter turnout was 78.7 percent, below the record 80 percent-plus the election overseer reported in October, when Chavez defeated Capriles 55 percent to 44 percent.
"We won a just, legal, constitutional election," Maduro told cheering red-shirted supporters from the balcony of Venezuela's Miraflores presidential palace as fireworks erupted around the capital, Caracas.
"If I had lost by one vote, I would have accepted my responsibility immediately," he said. "The electoral authorities said what the people wanted."
Capriles said he did not accept the results and called for an immediate recount.
"According to our count, we have a result other than that expressed tonight," he told supporters. He vowed to do everything in his power "under the Constitution" to ensure the true elections results are revealed.
Maduro told supporters he would welcome a recount.
Sunday's election came less than six weeks after Chavez, 58, died at a Caracas military hospital after a long battle with cancer.
Maduro, 50, is a former union activist with close connections to the Castro brothers in Cuba.
Capriles, 40, is a law graduate and former national legislator who is now governor of Miranda, Venezuela's second most-populous state.