Nigerian President Goodluck Jonathan urged his supporters on 1 April to follow "due process" in channeling their frustrations at losing this weekend's election, trying to pour cold water on any potential post-vote violence.

In a short concessional statement, Jonathan wished his opponent well and urged his supporters to keep their cool.

"Nobody's ambition is worth the blood of any Nigerian," he said in a statement issued after his election defeat. "The unity, stability and progress of our dear country is more important than anything else," said Jonathan in a televised broadcast statement.

Three decades after seizing power in a military coup, Muhammadu Buhari became the first Nigerian to oust a president through the ballot box, putting him in charge of Africa's biggest economy and one of its most turbulent democracies.

As the scale of this weekend's electoral landslide became clear, Jonathan called Buhari on Tuesday to concede defeat to the opposition leader, an unprecedented step that should help to defuse anger among Jonathan's supporters.

In the religiously mixed northern city of Kaduna, where 800 people were killed in violence after the last elections in 2011, Buhari supporters streamed onto the streets, waving flags and dancing and singing in celebration.

In an unprecedented step, Jonathan phoned Buhari to concede defeat and issued a statement urging his supporters to accept the result, a signal of deepening democracy in Africa's most populous nation that few had expected.

The 72-year-old general, who first came to power three decades ago via a military coup, campaigned as a born-again democrat intent on cleaning up the corrupt politics of Africa's most populous nation.

The margin of victory - Buhari got 15.4m votes to Jonathan's 13.3m - was enough to prevent any challenge. The rules state he must officially hand over on 29 May.

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