The election could calm a five-month political crisis in Honduras that began when the army overthrew Manuel Zelaya, the country's leftist president, and threw him out of the country.
But the votes legitimacy has already been challenged by Zelaya and his supporters.
Despite officials claims that voter turnout was over 60 per cent, Zelaya has insisted the true number was much lower.
Speaking to Al Jazeera, Zelaya said he had evidence that Hondurans had refused to turn out for the election and that the vote had "no respect and no credibility".
"We took a sample at the polls and the rate of abstentions was over 60 per cent in most cases," he said.
"This means the election had low turnout, which means it did not enjoy the support of the majority of the Honduran people."
Zelaya was speaking from inside the Brazilian mission in Tegucigalpa, the Honduran capital, where he has taken refuge since returning to the country several weeks ago.
"We are fighting a dictatorship and until we defeat it we will not be satisfied," Zelaya told Al Jazeera.
Tomas Andino, an activist for a group called the National Resistance Front, which is against Micheletti's administration, also said that turnout had been low.
"Anyone who has wandered about the city of Tegucigalpa or other cities of Honduras will realise that the number of people who went to the polls was really minimal," he told Al Jazeera.
Craig Mauro, Al Jazeera's reporter in Tegucigalpa, said turnout had been very low in the city's poorer districts where support for Zelaya is strongest, but had been much higher in wealthier areas.
Neither Zelaya nor the man who replaced him - Roberto Micheletti, the de facto president – ran in the vote and the election has been largely shunned by international monitors.
The US government said late on Sunday that it considered the Honduran election "a necessary and important step forward" toward resolving the country's political crisis.
But Lucia Newman, Al Jazeera's Latin America editor, said that, despite the vote, the crisis was still some way from being resolved.
"This is still a very divisive issue and there are still a lot of people who are bitterly unhappy about what has happened in this country since Manuel Zelaya was overthrown," she said.
"I think right now the main priority for many people in this country is to obtain the international credibility and legitimacy that this country needs in order to bring it back from what is basically international isolation."
Regional powers have been divided over whether or not to recognise the outcome of the election, with some Latin American countries such as Brazil, Venezuela and Argentina making clear they will not back the result.
Luiz Inacio Lula da Silva, Brazil's president, told reporters: "It's not possible to accept a coup, whether it's a military coup or dressed up as a civilian coup."
Tensions were high across Honduras ahead of the vote, but only small scale protests were reported.
The election was organised before Zelaya was removed from power, with the candidates chosen in primaries last year.
|Zelaya and his supporters have challenged
the legitimacy of the vote [Reuters]
"These elections would have been the same, whether Zelaya had been there or not," Edward Schumacher-Matos, a newspaper columnist and Latin America analyst, said.
"You had a constitutional crisis that was precipitated by the president himself," he told Al Jazeera in New York.
"He was ordered arrested by the supreme court for violating the constitution. He tried to carry out a referendum that the supreme court, the congress, his own attorney-general and the human rights ombudsman all said was a violation of the constitution and illegal."
Zelaya had called for a vote asking the public whether they would support attempts to remove the one-term limit for the presidency set out in the constitution.