BBC reporter Rana Jawad: "Liby was ambushed, according to his son, by four cars"
Al-Qaeda's remaining leaders
Al-Qaeda around the world
Libya's prime minister has called on Washington to explain a special forces raid on its territory, one of two by US commandos in Africa on Saturday.
Ali Zeidan's office said he had asked for clarification and stressed Libya was "keen on prosecuting any Libyan citizen inside Libya".
The raid captured al-Qaeda leader Anas al-Liby, who the US says is "currently lawfully detained outside of Libya".
The other raid was in southern Somalia but failed to capture its target.
The commando raid there was believed to have focused on a leader of the al-Shebab militant group, which says it carried out last month's attack on the Westgate shopping centre in the Kenyan capital, Nairobi, leaving at least 67 people dead.
Frank GardnerBBC security correspondent
This weekend's twin raids by US commandos to target America's enemies in Africa are the result of intensive planning by US intelligence agencies and Special Operations Command.
The Libyan jihadist snatched on Saturday had been on the FBI's wanted list since 2001. Once informants on the ground in Libya had confirmed his exact location, it would have been relatively easy for the US Army Delta Force commandos to deploy from a US base in Europe.
But targeting al-Shabab leaders believed responsible for the Nairobi Westgate attack has proved more difficult. Here, it seems US intelligence got it wrong on two counts: the wanted man was not at home and the Navy Seal commandos encountered far fiercer resistance than they had expected, forcing them to withdraw empty-handed.
What this shows, though, is that in an era where Washington is trying to avoid getting drawn into costly overseas wars, it is nevertheless prepared to launch pinpoint raids like these, despite accusations it may be breaking international law.
What did US raids achieve?
When asked on Sunday whether Somalia had been aware of the raid, Prime Minister Abdi Farah Shirdon Saaid said: "Our co-operation with international partners on fighting against terrorism is not a secret."
A press release posted on an official Libyan government website read: "The Libyan government is following the news about the Libyan citizen wanted by the US government.
"Since we've heard, we have been in touch with the US government and have asked for clarification on this matter.
"The Libyan government is keen on prosecuting any Libyan citizen inside Libya, no matter what the charges are... the accused are innocent until proven guilty."
The statement raises questions about how much, if anything, Libya knew in advance of the raid.
A US official had earlier been quoted by CNN as saying that the raid was conducted with the knowledge of the Libyan government.
Liby, 49, is believed to have been one of the masterminds behind the 1998 US embassy attacks, which killed more than 220 people in Kenya and Tanzania.
He has been indicted in a New York court in connection with the attacks.
Continue reading the main story
Born 30 March 1964 in Tripoli, Libya. Also known as Nazih Abdul-Hamed al-Ruqai
Believed to have joined al-Qaeda in 1990s
Given political asylum in UK
Rumoured to have returned to Libya during 2011 civil war
Charged by New York prosecutors in 2000 with involvement in the 1998 Kenya and Tanzania US embassy bombings
One of FBI's "most wanted terrorists" with $5m bounty for his capture
Profile: Anas al-Liby
Liby - whose real name is Nazih Abdul-Hamed al-Ruqai - has been on the FBI's most wanted list for more than a decade with a $5m (£3.1m) bounty on his head.
A Pentagon statement on Sunday said he was "currently lawfully detained under the law of war in a secure location outside of Libya".
It said: "The successful capture operation was made possible by superb work and coordination across our national security agencies and the intelligence community, and was approved by President Obama."
No American personnel were injured, it said.
Anas al-Liby was seized in Tripoli early on Saturday as he was parking outside his house.
Three vehicles encircled him, his car window was smashed and his gun was seized before he was taken away, his brother, Nabih, told the Associated Press news agency.
On Sunday he told reporters that the US operation was an "act of piracy".
Liby's son, Abdullah, said that those he could see taking his father looked Libyan and spoke a Libyan dialect. He said that some were masked.
US Secretary of State John Kerry said the operations in Libya and Somalia showed that the US would never stop "in its effort to hold those accountable who conduct acts of terror".
Those who attacked American interests "can run but they can't hide", he said.
The US defence department also confirmed that special forces had carried out a seaborne operation in Somalia's coastal town of Barawe on Saturday.
Libyans took to social networking sites to discuss the raid
Pentagon spokesman George Little said the forces had been "involved in a counter-terrorism operation against a known al-Shabab terrorist". He gave no further details.
Initial reports in the US media quoted unnamed US officials as saying that the suspect had been captured or killed by US Navy Seals in the pre-dawn raid on a villa.
However, the officials later said that the Seals failed to find the intended target, who was not identified.
Prime Minister Saiid said on Sunday: "We have collaboration with the world and with neighbouring countries in the battle against al Shabab... our interest is to get a peaceful Somalia, free from terrorism."
John Kerry: "Those members of al-Qaeda and other terrorist organisations can run but they can't hide"
The raid was carried out by members of Seal Team Six - the same unit that killed al-Qaeda leader Osama Bin Laden, a US military official told AP.
The official added that in Barawe the commandos had decided to abort the mission after encountering fierce resistance from al-Shabab fighters.
"The Barawe raid was planned a week and a half ago," a US security official told the New York Times.
"It was prompted by the Westgate attack," added the official, who was speaking on the condition of anonymity.
Al-Shabab earlier told the BBC that "white soldiers" had arrived by boat in Barawe and rebels had repulsed them, losing a fighter.