The meeting follows warnings from Nigeria and its neighbours that Boko Haram - which has killed thousands of Nigerians during its five-year-old insurgency, and last month kidnapped more than 200 schoolgirls - now threatens the security of the region.
Leaders from every corner of the continent would meet before South African President Jacob Zuma's inauguration on Saturday to "focus on collective action to effectively roll back the scourge of terrorism in Africa," spokesman Reuben Abati said.
As well as Boko Haram, regional and world powers are increasingly worried about the growing reach of groups such as al-Qaeda in the Islamic Maghreb and Somalia's al Shabaab, which has attacked Uganda and Kenya and this week threatened to unleash teenage suicide bombers in Nairobi.
Security experts say cross-border intelligence sharing between countries threatened by militant groups is woefully weak.
Jonathan and the military have been criticised in Nigeria for the slowness of their reaction to the mass abduction, which took place in the remote northeastern village of Chibok, near the borders of Cameroon and Chad.
Nigeria accepted help from the United States, Britain, France and China last week and around 80 U.S. troops were arriving in Chad to start a mission to try to free the schoolgirls.
Boko Haram, which is fighting to set up an Islamic caliphate in northern Nigeria, has stepped up attacks in recent weeks.
Since the day of the abductions, which have grabbed global attention, at least 425 civilians have been killed. A bomb blast at the edge of the capital Abuja killed 71 people on the same day of the kidnappings on April 14 and eight more girls have since been snatched.
Boko Haram initially attacked mostly security forces and government officials after it launched its uprising in northeast Borno state's capital Maiduguri in 2009.
But when Jonathan ordered a military offensive a year ago to flush them out, civilians formed vigilante groups to help out - and themselves became targets.
Suspected Boko Haram militants shot dead 29 farm workers as they tilled their fields in remote northeast Nigerian village of Chukku Nguddoa. A bomb blast in Jos killed 118 people on Tuesday, the deadliest single attack in the central city, which has been periodically targeted by Islamist bombers since 2010.
Nigerian protesters have taken to the street and launched a online campaign to press authorities to do more to free the girls. But on Thursday, Jonathan urged Nigerians to be realistic.
"We all must come together to fight terrorism ... protests should be directed at the terrorists," he said. "We must never lose sight of the fact that the terrorists are the real enemy."
The president has referred to Boko Haram as "al Qaeda in West Africa" seeking to portray what is often seen as a homegrown insurgency as part of a global jihad network.
Security officials say Boko Haram fighters have received training, arms and funding from both Somalia's al Shabaab and al Qaeda's wing in the Sahara, though they doubt links are extensive.
The governor of Borno state Kassim Shettima told Reuters in an interview late on Thursday that Boko Haram had many foreign fighters, including Chadians, Cameroonians, but also Libyans who fled after the fall of Muammar Gaddafi in 2011.
"If you call them Nigeria's al-Qaeda, you honour them. These guys are just plain raving lunatics," Shettima said.
The U.N. Security Council committee on al Qaeda sanctions blacklisted Boko Haram on Thursday.