With 42% of votes declared, the conservative Juan Orlando Hernandez leads with 34.15%, while Xiomara Castro has 28.45%, say election officials.
However, Xiomara Castro, wife of ousted ex-president Manuel Zelaya, has announced to reporters that she has won.
Turn-out was high in Honduras, with millions voting for a new president, members of parliament and local mayors.
Voting took place amid tight security, but no serious incidents were reported in Honduras, which has the highest murder rate in the world.
Polling was extended for one hour due to a big turn-out.
“Thank God and thank you to the Honduran people for this triumph,” posted Juan Orlando Hernandez on his Twitter page, at that stage with 24% of votes declared.
Xiomara Castro also used her Twitter account to announce that she had won: “Based on the exit poll results that I have received from the whole country, I can tell you: I am the president of Honduras.”
She is bidding to become the first female president of Honduras
“Today, we can say that we have won,” Xiomara Castro told reporters.
David Matamoros, president of the electoral court, said final results were not expected until early Monday.
“The preliminary results we have given so far do not show any tendency or declare any winner,” he said.
Opinions polls had pointed to a close race between Xiomara Castro and Juan Orlando Hernandez, the two leading candidates in the presidential race.
Juan Orlando Hernandez, whose National Party backed the military coup in 2009 against Manuel Zelaya, has vowed to restore order with more soldiers and police on the streets.
Xiomara Castro has proposed a community police force to tackle local crime, with more soldiers deployed to the borders to combat drug trafficking.
Around 5.4 million Hondurans were registered to vote and authorities say there was a “massive turn-out”.
Honduras is one of the poorest countries in Latin America. It also has the world’s highest murder rate, averaging 20 a day.
Much of the violence is blamed on gang violence and drug traffickers.
A margin of just one vote is needed for a win – there is no run-off election.
nWnhYbcuxXYQuincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…
Misleading allegations, rumours and outright lies about voting and fraud are flooding online spaces in…
At least 158 people have died in Spain's worst flooding disaster in generations. On October…
Google has been fined two undecillion (a two followed by 36 zeroes) roubles by a…
Embarking on a home remodel is an exciting journey, promising enhanced comfort, increased property value,…
The US presidential candidates continued to campaign across key swing states on October 20. Footage…