He said Nigeria was still struggling to come to terms with the suffering of the 1967 conflict when the south-east tried to establish the state of Biafra.
Tens of thousands of people have fled the recent post-poll unrest.
The president said the violence was intended to frustrate remaining polls, but they would go ahead.
However, elections for powerful state governors will be delayed for two days, until Thursday, in two of the worst affected states - Kaduna and Bauchi, the electoral commission announced.
Riots broke out in the north on Monday after Mr Jonathan, a southerner, emerged as the winner of the presidential poll.
Former military ruler Muhammadu Buhari, who is popular in the north, denies instigating the "sad, unfortunate and totally unwarranted" events.
Nigeria is divided by rivalry between the predominantly Muslim north and the mainly Christian south, which also have cultural, ethnic and linguistic differences.
Mr Jonathan's People's Democratic Party (PDP) has previously alternated its presidential candidate between people who come from each of the two halves of the country, in an attempt to keep the peace.
Continue reading the main story goodluck Jonathan, People's Democratic Party: 22.5 million votes (59.6%)muhammadu buhari, Congress for Progressive Change: 12.2 million votes (32.3%)nuhu ribadu, Action Congress of Nigeria: 2.08 million votes (5.5%)Ibrahim Shekarau, All Nigeria Peoples Party: 911,455 votes (2.4%)Figures: Independent National Electoral Commission
'enough is enough' In an address to the nation, President Jonathan said the "horrific acts" of the last few days had been shocking."They killed and maimed innocent citizens." "they set ablaze business premises, private homes and even places of worship," he said.
"If anything at all, these acts of mayhem are sad reminders of the events which plunged our country into 30 months of an unfortunate civil war," he said referring to the Biafran war in which more than one million people died.
"As a nation we are yet to come to terms with the level of human suffering, destruction and displacement, including that of our children to far-away countries, occasioned by those dark days."
"enough is enough," he said.
The BBC's Abdullahi Abubakar Kaura in Kaduna, the state which has witnessed the worst of the violence, says Kaduna city is now calm.
But it is difficult to confirm what is happening in the south of the state where there have been reports of continuing disorder.Kaduna's police say 32 people have died in the clashes - our reporter says the casualty figure may rise as Muslims tends to bury their dead quickly - sometimes before their deaths are officially reported.
He went to one hospital in the city and saw 25 charred corpses on a mortuary floor and was told there were another 25 bodies in the mortuary fridge but he had to leave without checking because of the stench.
On Wednesday, the Red Cross put the figure of those fleeing the violence at 48,000.
'dastardly acts'During his speech, the president said that security has been reinforced nationwide to quell any further unrest.
He added that there was no grievance that the law courts could not address.
Calm has returned to most areas but many people have fled fearing more violenceGen Buhari has said that his party will challenge some of the results - he maintains the election commission's computers were programmed to disadvantage his party in some parts of Nigeria.
But he urged his supporters to refrain from attacks, saying: "It is wrong for you to allow miscreants to infiltrate your ranks and perpetrate such dastardly acts as the mindless destruction of worship places."
"needless to say, this act is worse than the rigging of the elections."
International observers have said the election was reasonably free and fair.
Mr Jonathan, a Christian from the oil-producing Niger Delta, was appointed to the presidency last year upon the death of incumbent Umaru Yar'Adua ' Watch, a northern Muslim whom he had served as Vice President.
He staked his reputation on the election, repeatedly promising it would be free and fair.
To win at the first round, a candidate not only needs the majority of votes cast, but at least 25% of the vote in two-thirds of Nigeria's 36 states. Goodluck Jonathan, of the PDP, reached that threshold in 31 states; Runner-up Muhammadu Buhari of the CPC only did so in 16 states.
Nigeria's 160 million people are divided between numerous ethno-linguistic groups and also along religious lines. Broadly, the Hausa-Fulani people based in the north are mostly Muslims. The Yorubas of the south-west are divided between Muslims and Christians, while the Igbos of the south-east and neighbouring groups are mostly Christian or animist. The Middle Belt is home to hundreds of groups with different beliefs, and around Jos there are frequent clashes between Hausa-speaking Muslims and Christian members of the Berom community.
Despite its vast resources, Nigeria ranks among the most unequal countries in the world, according to the UN. The poverty in the north is in stark contrast to the more developed southern states. While in the oil-rich south-east, the residents of Delta and Akwa Ibom complain that all the wealth they generate flows up the pipeline to Abuja and Lagos.
Southern residents tend to have better access to healthcare, as reflected by the greater uptake of vaccines for polio, tuberculosis, tetanus and diphtheria. Some northern groups have in the past boycotted immunization programs, saying they are a Western plot to make Muslim women infertile. This led to a recurrence of polio, but the vaccinations have now resumed.
Female literacy is seen as the key to raising living standards for the next generation. For example, a newborn child is far likelier to survive if its mother is well-educated. In Nigeria we see a stark contrast between the mainly Muslim north and the Christian and animist south. In some northern states less than 5% of women can read and write, whereas in some Igbo areas more than 90% are literate.
Nigeria is Africa's biggest oil producer and among the biggest in the world but most of its people subsist on less than $2 a day. The oil is produced in the south-east and some activist groups there want to keep a greater share of the wealth which comes from under their feet. Attacks by militants on oil facilities led to a sharp fall in Nigeria's output during the last decade. But in 2010, a government amnesty led thousands of fighters to lay down their weapons.
