The Supreme Court hearing had been expected to take place on Thursday but was delayed when the outgoing president called a two-day public holiday
Electoral officials previously said the 61 million ballots have already been printed, but that unspecified provisions had been made in case Abubakar should rejoin the field.
"I have scored a moral victory, I have scored a legal victory, I have scored a constitutional victory, I have scored a democratic victory," Abubakar told Al Jazeera.
"I am confident I can win on a free, fair and level playing field basis. But the way things are going in Nigeria ... I have no faith in the election commission because there is a conspiracy to turn Nigeria into one party rule, a one party state, therefore a dictatorship."
The electoral commission barred Abubakar from the ballot after an executive panel established by the president found Abubakar stole government funds. Abubakar denies the fraud allegations.State elections
Saturday's presidential poll comes after state elections were marred by violence and allegations of vote rigging.
|"I have no faith in the election commission because there is a conspiracy to turn Nigeria into one party rule, a one party state, therefore a dictatorship"|
Atiku Abubakar, presidential candidate for the Action Congress
An observer team from the west African bloc ECOWAS said the state elections were "relatively free and peaceful
But the head of the mission, Dauda Jawara, former Gambian president noted however that voting did not start on time in many centres and that the security of electoral materials was "compromised"' as they were transported with few or no escorts.
He also said many polling stations were located in unsuitable locations making it difficult to ensure secret ballots and that the collapsible plastic boxes, which had zips rather than seals, were susceptible to abuse and vandalism.
The People's Democratic Party (PDP) of Olusegun Obasanjo, the current president, have dominated the results in the state governship elections, winning 20 out of the 26 announced by Monday.
The PDP, which has controlled 28 of the country's 36 states since May 1999, is expected to win the majority of the remaining 10 states.
Philip Umeadi, Independent National Electoral Commission (INEC) spokesman, said results from nine states were still to be released while the vote in the southeastern state of Imo had been cancelled because of irregularities.
He said a new poll would take place on April 28, one week after the presidential and national assembly elections.
Abubakar's party dismissed the results as fraudulent.