(CNN)Incumbent Goodluck Jonathan phoned former military leader Muhammadu Buhari on Tuesday to concede defeat in Nigeria's presidential elections, Buhari's party says. Jonathan acknowledged the phone call and his defeat in a written statement to his countrymen. "I thank all Nigerians once again for the great opportunity I was given to lead this country and assure you that I will continue to do my best at the helm of national affairs until the end of my tenure," he said. The Independent National Electoral Commission is still announcing the final tally in the polls, but early numbers indicate Buhari, now the President-elect, has an overwhelming majority of votes. Buhari ruled Nigeria from late 1983 until August 1985 after ousting his predecessor in a coup. His 20-month rule was known for what he described as a "war on indiscipline," a tough regime that some say was marred by human rights abuses. The 72-year-old  retired major general's experience as a military ruler has variably been viewed as a plus or minus in present-day Nigeria, where the government has been locked in a deadly battle with the militant group Boko Haram. His campaign has focused on security and ending corruption in Nigeria. Read more: Who is Nigeria's Muhammadu Buhari? Violent protests after elections Saturday sparked calls for calm from the two main candidates and a warning by the United States and Britain against political interference. Demonstrators fired gunshots and torched a local electoral office in Nigeria's oil-rich Rivers state on Sunday as they marched to protest the elections amid claims of vote-rigging and voter intimidation. After the protests in Rivers, Buhari's All Progressives Congress demanded the elections there be canceled. "There's been so much violence in Rivers state that it's just not tenable," party spokesman Lai Mohammed said. But the People's Democratic Party disputed the accusation, saying the election was "credible and the result reflects the overwhelming wish of the people of Rivers state to support President Goodluck Jonathan." Both candidates took to social media to call for calm. "I want to urge all Nigerians to also wait patiently for the Independent National Electoral Commission, INEC, to collate and announce results," Jonathan said on his Facebook account. "Fellow Nigerians, I urge you to exercise patience and vigilance as we wait for all results to be announced," Buhari said on Twitter. Jonathan and  Buhari last week issued a pledge reaffirming their commitment to "free, fair and credible elections" after their signing of  the Abuja Accord in January. In his statement Tuesday, Jonathan said; "I promised the country free and fair elections. I have kept my word." He advised anyone upset with the results to follow due process and stay away from further violence. "As I have always affirmed, nobody's ambition is worth the blood of any Nigerian. The unity, stability and progress of our dear country is more important than anything else," he said. Read more: Democracy was the real winner . More than 800 people were killed in post-election violence across Nigeria's north in 2011 after charges that those elections were illegitimate. Nigeria's vote had been scheduled for February 14, but on February 7, Nigeria's election commission announced it would be postponed for six weeks because of security concerns, with the military needing more time to secure areas controlled by Boko Haram. The controversial decision was unpopular among many Nigerians and led to widespread protests. Jonathan has been criticized for not doing enough to combat Boko Haram, which is waging a campaign of terror aimed at instituting a stricter version of Sharia law in Nigeria. On Saturday, residents in the northeastern state of Gombe said at least 11 people were killed and two more injured in attacks at polling stations, apparently by Boko Haram extremists. CNN's Christian Purefoy reported from Lagos, Nigeria, while CNN's Susannah Cullinane and Stephanie Busari wrote from London.
Incumbent President Goodluck Jonathan acknowledges defeat, says he delivered on promise of fair elections . Muhammadu Buhari's party says Jonathan called to concede even before final results are announced . Buhari is a 72-year-old retired major general who ruled in Nigeria in the 1980s .