President Edgar Lungu, of the governing PF party, holds a slim lead over his rival Mr Hichilema, with votes counted in more than 80% of constituencies.
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Earlier, his UPND party withdrew from the ballot verification process, alleging fraud.
Officials of the ruling party nap as they await results of the presidential elections in Lusaka, Monday, Aug. 15, 2016.
Lungu defeated Hichilema in the previous election, last year, by less than 28,000 votes.
Lungu was elected in January 2015 after the death of the incumbent president, Michael Sata.
But PF secretary general Davis Chama, who popped several champagne bottles at Mulungushi Conference Centre where the results were announced, laughed off allegations that the vote was rigged.
The 54-year-old said when he voted that he would accept the election result if it was “free, fair and transparent”. “This has been reported to the police and we are waiting to see how the police will react”.
However, the run-up to polling was characterized by violence between the rival parties. The percentage turnout of voters was 56.
Lungu will rule for a second five-year term.
Campaigning for this week’s vote centered on the economy, after months of rising unemployment, mine closures, power shortages and soaring food prices in Africa’s No. 2 copper producer.
The victor of Thursday’s election must get more than 50 percent of the vote to avoid a runoff.
“Furthermore, the president had allowed his ministers to remain in office after the dissolution of parliament so that they could use public resources – to the detrimental of us in the opposition – during the campaign period”, he said.
Known as “HH”, Hichilema has major investments in ranching, property and healthcare in Zambia.
Growth was more than 10 percent in 2010.
About 60 percent of the population live below the poverty line, according to the World Bank.
The constitution has now been amended so that the vice-president automatically takes office if a sitting president dies.
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Electoral officials have warned political parties against making such statements, but all parties have access to the raw voting data and may add up the results faster than the national commission.
