Violence was reported in mostly Muslim Kano, Zaria and Kaduna, where a church was set on fire, a witness told CNN.
Jonathan, a Christian southerner, won more than the required 25 percent of the vote in two-thirds of the 36 states and a majority nationwide, said his campaign aide, Ken Okolugbo.
The Independent National Electoral Commission's running tally showed Jonathan far ahead, and official results were expected later Monday.
The Nigerian Tribune reported earlier that Jonathan, of the Peoples Democratic Party, had more than 22 million votes, while his main rival, former military dictator Muhammadu Buhari of the Congress for Progressive Change, had 12 million.
Jonathan had been vice president and took over when President Umaru Yar'Adua died last year.
Saturday's voting was largely peaceful, following violent parliamentary elections on April 9.
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