About midday in Honduras on Monday, the electoral authority's website showed Asfura - the conservative National Party candidate backed by US President Donald Trump - leading Liberal Party candidate Nasralla by just 515 votes.
It was not clear how many votes had been counted due to problems with the electoral portal.
Rixi Moncada, of the ruling LIBRE Party, was well behind in third with 19 per cent of the vote.
Nasralla posted on X that internal projections put him ahead with 44.6 per cent.
"We are not declaring ourselves the winners, just projecting the results that will be fed into the CNE (electoral body) in the next hours," he said in the post.
Members of the National Party criticised Nasralla for not waiting until final results had been released by the electoral authority.
CNE President Ana Paola Hall, in a post on X, called for calm amid the technical tie and asked for patience as the count continues.
Asfura's lead has narrowed significantly since the first preliminary results were released on Sunday evening.
Trump responded to the changing margin by saying it appeared Honduras was "trying to change the results of their presidential election", alleging that the country's election commission prematurely stopped counting votes.
"If they do there will be hell to pay! The people of Honduras voted in overwhelming numbers on November 30th," Trump said on his Truth Social platform.
Outgoing President Xiomara Castro reposted on X a message from her husband, former president Manuel Zelaya, calling for vigilance while "awaiting the final count, with 100 per cent of the presidential ballots tallied".
Throughout Monday morning, problems with the online portal where results were meant to be updated added to frustration around the vote.
The website appeared to be down for long stretches, with local media criticising the outage.
In the run-up, Trump weighed in on the tightly contested race to throw his support behind Asfura, 67-year-old former mayor of Tegucigalpa, in a series of social media posts, saying he can work with him to counter drug trafficking and that "if he doesn't win, the United States will not be throwing good money after bad".
On Friday, Trump also said he would grant a pardon to former Honduras President Juan Orlando Hernandez, who is serving a 45-year prison sentence in the US for drug trafficking and firearms charges.
Hernandez, who led Honduras from 2014 to 2022, was also from the National Party.
Sunday's vote, in which the 128 members of Congress, hundreds of mayors, and thousands of other public officials are also being chosen, took place in a highly polarised climate.
Moncada has suggested she would not recognise the official results.
Most polls showed a virtual tie between the three candidates heading into election day.
The Organization of American States expressed concerns about the electoral process.
Honduras, where six out of every 10 citizens live in poverty, suffered a coup in 2009 when an alliance of right-wing military figures, politicians and businessmen overthrew Zelaya, who was a Liberal Party member at the time.
In 2011, Zelaya founded the Libertad y Refundacion party, with which his wife swept to power in 2021, ending more than a century of rule by the National and Liberal parties.
