Nigeria president visits site of first suicide blast
"The security agencies are on top of it," Jonathan told reporters after his inspection of the site.
"Surely, we will get over it. People should not be panicky at all. Soon, most of these things will be a thing of the past," he said.
He was conducted round the site by national police chief Hafiz Ringim, whom Boko Haram said was the target of its attack.
"Let me use this opportunity to assure Nigerians that it is a period globally, that we experience all these terrorist attacks all over the world. No country is free," Jonathan said.
"Nigeria is also having some ugly incidents relating to that."
The explosion is the latest in a series of deadly attacks in recent months, adding to a climate of insecurity just weeks after Jonathan's election late April for his first full term.
Security experts said it was the first suicide bombing in Nigeria, a country of 150 million people facing a growing threat from Islamic militants.
Police were tracking down the perpetrators, police spokesman Yemi Ajayi said.
"We will leave no stone unturned," he told AFP. "We already suspected Boko Haram over the attack. So we are not surprised that they claimed responsibility for it."
Boko Haram said it regretted missing its target, the police chief.
In a statement, the group referred to comments the police chief had made days earlier, faulting him for "unguarded utterances to the effect that he will crush us in a matter of days."
Police said the bomber drove into the car park and set off the bomb as he was about to be submitted to a routine search. Local media say the bomber was trailing the police chief as he drove into the compound.
Boko Haram, sometimes called the Nigerian had warned Wednesday of "fiercer" attacks.
Boko Haram, which means "Western education is sin", launched an uprising in 2009 which was put down by a brutal military assault that left hundreds dead, mostly sect members.
Boko Haram also claimed responsibility for a spate of bombings near Abuja and in the north, claiming 18 lives, after Jonathan's inauguration about two weeks ago.
Copyright AFP (Agence France-Presse), 2011