In an exclusive interview with The Independent, 63-year-old General Obasanjo said: "More than 17 million Nigerians voted for me. If I am regarded as having been installed by the military then those 17 million people must be military."
Earlier Mr Falae, whose alliance was also accused of election fraud, called for a government of national unity. He planned a legal challenge to the result - 62.78 per cent for General Obasanjo against his 37.22 per cent.
General Obasanjo, who was military head of state for three years from 1976, is best known internationally for having handed power to a civilian in 1979.
But in a country ruled by junta for all but 10 of its 39 years of independence, there are fears that he will preside over a "military democracy" overseen by generals. He will be formally installed for his four-year term on 29 May.
Throughout his campaign, General Obasanjo was reticent when questioned and his rhetoric, such as it was, won him no admirers in the international media. He even failed to turn up for the televised election debate, allegedly because the questions were not provided in advance.
Yesterday, the general, as he is called by his aides, was equally unforthcoming, staring at the floor during answers, responding only in vague terms, and ill-at-ease with the spontaneous nature of interviews.
But he relished being asked how he should be addressed in future. He stood up, wearing a pale blue agbada (traditional robe) and silver embroidered bonnet, and raised his voice: "You can call me President Olusegun Obasanjo or President Chief Olusegun Obasanjo or, of course, President General Olusegun Obasanjo."
He was vague about his priorities and backtracked on a pre-election pledge to withdraw Nigerian troops immediately from intervention force duties in Sierra Leone. "Nigeria will always play a part in peace-keeping but we have to see what we can best do without straining our own resources," he said.
All day the general received well-wishers at a suite in the Hilton Hotel in the capital, Abuja, including prominent businessmen who had given financial support.
But he faces glaring economic and social problems, extensive corruption and deepening poverty in tandem with a falling oil price.
The general said: "People talk about economic and social problems without going back to basics. The basic problem is political. Unless we deal with political issues, we will not make headway on economic issues."
Apparently referring to regional rivalries and conflicts, he added: "I will stretch out my hands of welcome to all Nigerians, no matter what has happened during the election process, until everyone feels they have a stake and belongs to Nigeria.
"Once this process is complete, it will be all hands on deck to eradicate corruption and for people to feel that justice and equity will be done.
"Then we can address issues like communications, energy, lack of water, education, health and the security of life and property. You can see how politics and issues all hang together," he said.
General Obasanjo has three months to complete the transition process in co-operation with the military head of state, General Abdulsalami Abubak- ar. Yesterday, the Abubakar government finally announced a constitution would be published, probably this week.
The lack of such a document during the election process has been sharply criticised by local and international observers, led by the former United States president Jimmy Carter.
Mr Carter, who headed a delegation of observers, told Nigerian election officials that fraud was so widespread it was impossible to judge whether the results were accurate, though the United States did congratulate Nigeria on a peaceful election, saying it "broadly reflected the will of the Nigerian people". Clement Nwankwa, director of the Constitutional Rights Project, an observer group, said: "The publication now of the constitution confirms one of our worst fears - that the military was waiting to see who would win the election before deciding which constitution to give us."
The Constitutional Rights Project, other pro-democracy groups and international observers released extensive details of election fraud during the election. These included a turnout in the southern Bayelsa State of 122.66 per cent when, in fact, the general impression was of scepticism and lack of interest in voting. The 10,000 local observers reported several cases of polling station officials being led away at gunpoint while their ballot boxes were stuffed. In Kaduna, 50 children in school uniform were accredited to vote by a teacher. In Kano, in the north, people were said to be selling their votes for 10 naira (6p) and in the oil-producing Niger delta region, monitors said that 30 minutes after an empty ballot box was placed on a polling table, 600 votes were found inside it.
t At least one person was killed and four others injured when mobs of youths attacked and destroyed two police stations in Lagos with gasoline bombs. Both stations are in strongholds of Olu Falae, who lost the election.
Dozens of prisoners were released by the attackers, who smashed the cells with sledgehammers. At one station, police responded with gunfire and then tried to flee. The mob dragged officers out of the burning building and savagely beat four of them, cutting off the hand of a woman officer.
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