U.N. Secretary General Ban Ki-moon said the final casualty toll was likely to be high and Nigerian President Goodluck Jonathan ordered tighter security around the capital after what he called a "most despicable assault."
"This was an assault on those who devote their lives to helping others," Ban said in a statement. "We condemn this terrible act, utterly."
Body parts were strewn on the ground as emergency workers, soldiers and police swarmed around the building, cordoned roads and rushed the wounded to hospital.
"Different people have been taken to different hospitals so we're not sure of casualty figures. It is at least 18," said Mike Zuokumor, Abuja police commissioner.
Norway's government said a Norwegian citizen was among the dead. She was named as Ingrid Midtgaard, a 30-year-old lawyer employed by the United Nations.
"We cannot give an update at the moment, our people are around all the hospitals working hard," a Red Cross spokesman said.
It is difficult to get confirmation of attacks by Boko Haram because the group has an ill-defined command structure and a variety of people who speak on its behalf. The police and the government have not said who was responsible.
Speaking before the BBC report, an Abuja-based security source said he suspected Boko Haram, whose strikes have grown in intensity and spread further afield, or al Qaeda's North African arm.
In Friday's attack the car slammed through security gates of the U.N. complex, crashed into the basement and exploded, sending vehicles flying and setting the building ablaze.
"When the car got inside it went straight to the basement and exploded, killing people in reception, right and left," said Abuja resident James John, who saw the attack.
"The entire building, from the ground floor to the topmost, was just fire and smoke. I saw six bodies being carried."
Michael Ocilaje, a U.N. employee at the complex, said: "All the people in the basement were killed. Their bodies are littered all over the place."
The building was blackened from top to bottom. In places, walls were blown away and reduced to rubble.
British Prime Minister David Cameron spoke on Friday to Ban and President Jonathan to pass on his condolences.
"The Prime Minister described it as an appalling attack. He said Britain and Nigeria faced a common threat in Islamic extremism, and offered to do all we could to help find the perpetrators," a British spokesman said.
The Addis Ababa-based African Union condemned what it called "these abhorrent and criminal attacks which cannot be justified under any circumstances."
SIMILAR ATTACK
Militant attacks in the oil-producing regions of southern Nigeria have subsided but the north has been hit by a round of bombings and killings by Islamist extremists.
Boko Haram, whose name translates from the northern Hausa language as "Western education is sinful," has been behind almost daily bombings and shootings, mostly targeting police in the northeast of Africa's most populous nation.
The group claimed responsibility for a June bomb attack on the car park of the Abuja police headquarters which bore similarities to Friday's blast.
In the June attack, a car rammed through the gates of the police headquarters and exploded, killing the bomber and narrowly missing the chief of police.
Boko Haram's ambitions are growing and if it is confirmed to be responsible for Friday's attack, this would mark a shift beyond domestic targets.
In London, Henry Wilkinson of Janusian risk consultants, told Reuters: "This attack will prompt many Western organizations and business to reassess the threat the group poses."
"The targeting of the U.N. building indicates a more global outlook probably influenced by al Qaeda ideology."
In Abuja President Jonathan ordered tighter security.
"The President believes that the attack is a most despicable assault on the United Nations' objectives of global peace and security, and the sanctity of human life to which Nigeria wholly subscribes," a government statement said.
Security sources and diplomats are concerned that Boko Haram has links with more organized groups outside Nigeria.
These include Al Qaeda in the Islamic Maghreb which operates over the border in Niger and has kidnapped foreign workers there. It was also suspected of kidnapping a Briton and an Italian in Nigeria earlier this year.
In December 2007, a car bombing at the U.N. building in Algiers killed at least 41 people. In 2003, 15 staff and seven others were killed by a bomb attack at the U.N. building in Baghdad.
(Additional reporting by Joe Brock in Lagos, Robert Evans and Tom Miles in Geneva, Peter Apps and William Maclean in London, Patrick Worsnip at the United Nations; Editing by Angus MacSwan)