Yar'Adua was the hand-picked successor to President Olusegun Obasanjo, who admitted there was fraud and violence, in the voting but not enough to redo Saturday's election.
"Nothing should be done to make our people lose faith in the electoral process and its democratic outcome," Obasanjo said on national television.
Yar'Adua, of the ruling People's Democratic Party, won the election with 24,638,063 votes against 6,605,299 for his nearest rival, Muhammadu Buhari of the All Nigeria People's Party, Nigerian electoral officials reported Monday.
Buhari called for a rerun, while observers from the European Union called for urgent action, but did not say if the election should be held again, the London-based Financial Times reported.
Nearly 65 people died in violence related to the election and police continued to ban all protest rallies Monday.