With 80.29 per cent of votes counted, the Liberal Party's Nasralla held 40.23 per cent, less than 14,000 votes ahead of the National Party's Asfura, who had 39.69 per cent.
Rixi Moncada of the ruling leftist LIBRE Party was well behind in third place with 19.01 per cent.
System outages have beset the impoverished Central American nation's fiercely contested election since it took place on Sunday, and US President Donald Trump, who has strongly backed Asfura, has alleged election fraud, without providing evidence.
The delay in updating the vote tallies on Wednesday was the second such stoppage, with members of the electoral council blaming the company behind the tabulating platform for the outages.
The Honduran presidency is decided in a single round, and the candidate with the most votes wins, even if the margin is narrow or they fall short of an absolute majority.
Wednesday's counting halt was due to system maintenance that was done without proper notice, electoral council official Cossette Lopez-Osorio said on X, adding she considered it "inexcusable."
Nasralla remained confident despite the problems, writing on X: "Either way we're going to win."
Election observers from the European Union and the Organisation of American States as well as Honduras' electoral authority have called for calm and patience as the final votes are counted.
Early preliminary results released on Monday had originally shown Asfura with a slim lead of some 500 votes. Election organisers declared a "technical tie" and said votes would have to be counted by hand. When the count was updated on Tuesday, Nasralla had swung to a narrow lead.
The electoral authority later said a problem with the initial rapid count had failed to process 20 per cent of the votes.
Mark Weisbrot, co-director of the Center for Economic and Policy Research, a Washington-based think tank that promotes democracy, said Trump's comments and accusations against Asfura's rivals had undoubtedly had an impact.
Trump's threat to cut funding if Asfura did not win "would be considered likely to cause economic harm to Honduras and its people," he said.
On Monday night, Trump said on his Truth Social account that Honduras was "trying to change the results of their Presidential Election."
Moncada, the ruling party candidate, told Telesur the vote transmission system was flawed and criticised it as lacking transparency.
Referring to Trump's accusations of fraud, which she said violated international protocols, Moncada said this marked "a direct intervention that affects the interests of the Honduran people."
