Electoral Commission of Zambia figures showed Sata with 42 percent of the vote to 36.4 percent for President Rupiah Banda of the Movement for Multiparty Democracy, The Wall Street Journal reported. Other candidates had insignificant shares of the vote. The percentage of the total votes counted wasn't reported.
The BBC said that with 116 of 150 districts counted Sata had 44 percent of the vote to 36 percent for Banda.
The presidency goes to the candidate with the highest total in the first-past-the-post vote.
The election was held Tuesday but results have been delayed. Young men angry over the protracted count rioted Wednesday in Kitwe and Ndola, small cities in the copper-mining belt, Martin Malamba, a police chief in the region, said.
The High Court in Lusaka issued an injunction Thursday against news organizations publishing early election results, saying it wanted to prevent "speculative stories." Some members of the opposition say they are worried Banda is trying to rig the election results.
Zambia is Africa's biggest copper producer and a major focus of Chinese investment, which Sata opposes.
The European Union Election Observation Mission released a statement saying the election so far appeared to be "organized in a transparent and credible manner." The group said it would not make any final conclusion until the counting is over and results have been accepted.
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