First results on Sunday indicated that the ruling People's Democratic Party (PDP) would come out on top in both the presidential and legislative elections.
Umaru Yar'Adua, president Olusegun Obasanjo's chosen successor and a little-known state governor, is favourite to win.'Very disappointing'
Muhammadu Buhari, the country's former military ruler and another of the front-runners, said he would not accept the results and called for Obasanjo to be impeached.
"How many elections on the African continent have ever been fair?"
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"We will not accept it. Clearly there was no election in more than half of the states," he said.
In Buhari's home town, of Daura in northern Katsina, youths angered by the lack of ballot papers went on the rampage and burnt down six houses belonging to people close to the ruling party.
The local monitoring group said that the national electoral commission had not been adequately prepared for the vote and that this had led to chaos on election day.
"In many parts of the country elections did not start on time or did not start at all," he said.
Polling was marred by violence and accusations of corruption, vote-rigging and incompetence.
But the presidential election commisioner has defended the process.
"There was a lot of agitation ... that something fishy must be going on, which is not true," Alh Kabir Ahmen told Al Jazeera.
"In any country all over the world you can never get 100 per cent satisfaction. If it is largely free, fair and credible the result will stand."
European Union observers have also expressed concern about Saturday's vote. "For now the assessment is outspokenly negative ... I'm very concerned," Max van den Berg, the head of the EU mission, said.
One group of observers said that at one polling station in Yenagoa, in the oil-rich south, where 500 people were registered to vote, more than 2,000 votes were counted.
The government responded to criticisms of the poll by accusing Ken Nnamani, the senate president, of trying to incite chaos and impose an interim government on the country.
Nnamani, the third most senior state official, dismissed what he called "trumped up" charges and said he would never support a coup.
"These people have no shame," he told Reuters news agency, saying the conduct of the election had damaged Nigeria's role as an example for other African counties.
Source: Al Jazeera and agencies