Nigeria election: Goodluck Jonathan appeals for calm
Incumbent Mr Jonathan has been declared winner in the presidential poll, with the electoral commission saying he received about 57% of the vote.
Rioting spread across the Muslim north - the opposition's powerbase - as the outcome became clear.
International observers have said the election was reasonably free and fair.
But supporters of Mr Jonathan's main rival, Muhammadu Buhari, allege ballot-rigging.
The Red Cross says it believes many people have been killed in clashes with the police in northern areas of the country.
Homes of supporters of Mr Jonathan, a Christian from the oil-producing Niger Delta and the candidate of the governing People's Democratic Party (PDP), were attacked in the cities of Kano and Kaduna.
The BBC's Caroline Duffield, in the Nigerian capital Abuja, says General Buhari himself has yet to comment - but political pressure is growing on him to call for calm as well.
In a statement, Mr Jonathan said: "I have received with great sadness the news of sporadic unrest in some parts of the country which are not unconnected with last Saturday's elections.
"I appeal to those involved to stop this unnecessary and avoidable conduct, more so at this point in time when a lot of sacrifice has been made by all the citizens of this great country in ensuring the conduct of free and fair elections.
"I call on all our political leaders, especially the contestants, to appeal to their supporters to stop further violence in the interest of stability, peace and well-being of this great country.
"No-one's political ambition is worth the blood of any Nigerian."
Nigeria's Independent National Electoral Commission released final results later on Monday, saying Mr Jonathan had won 22.5 million votes to General Buhari's 12.2 million votes.
Mr Jonathan was appointed to the presidency last year upon the death of incumbent Umaru Yar'Adua, whom he had served as vice-president. He staked his reputation on the election, repeatedly promising it would be free and fair.
See www.bbc.co.uk