With 87.84 per cent of ballots tallied, Asfura of the National Party had 40.20 per cent, about 20,000 votes ahead of centrist rival Salvador Nasralla of the Liberal Party, who stood at 39.48 per cent, according to the electoral authority.
Rixi Moncada of the ruling leftist LIBRE Party remained well behind in third place on 19.31 per cent.
Some 14 per cent of ballots showed inconsistencies, officials said, and would be reviewed.
"Democracy is on trial in this election in Honduras. The Honduran people deserve to have their will respected and voices heard," Deputy Secretary of State Christopher Landau said on X. "The world's eyes, including ours, are on Honduras."
Trump has repeatedly intervened in the race, endorsing Asfura and alleging fraud without providing evidence.
Nasralla, a three-time presidential hopeful who identifies as centre-right, told Reuters that Trump's surprise endorsement last week of the conservative Asfura had flipped the race, and he rejected Trump's label of him as a "borderline communist."
Trump's backing of Asfura, experts say, fits in to his push to shape a conservative bloc across Latin America, stretching from Nayib Bukele in El Salvador to Javier Milei in Argentina. Trump also pardoned former National Party leader Juan Orlando Hernandez, who was serving a 45-year US sentence on drug trafficking and weapons charges.
Contested Honduran elections - such as in 2017 - have previously led to massive street protests and state violence, but Tegucigalpa remained calm on Friday as citizens awaited final results.
Honduras elects its president in a single round. The candidate with the most votes wins, even if the margin is narrow or the candidate falls short of a majority.
The electoral authority, known as the CNE, has called for calm and patience while the final votes are counted and inconsistent ballots reviewed.
