US Secretary of State John Kerry has defended the capture of an alleged al-Qaeda leader, Anas al-Liby, calling him a "legal and appropriate target".
He is a suspected mastermind of the 1998 US embassy attacks in Africa.
His son, Abdullah al-Ruqai, said his father was seized by masked gunmen and that some of them were Libyans.
Mr Kerry's comments come after Libya called on the US to explain the raid on its territory, one of two by US commandos in Africa on Saturday.
Mr Kerry said Anas al-Liby, who has been on the FBI's most wanted list for more than a decade with a $5m (£3.1m) bounty on his head, would face justice in a court of law.
"With respect to Abu Anas al-Liby, he is a key al-Qaeda figure, and he is a legal and an appropriate target for the US military," Mr Kerry told reporters on the sidelines of an Asia-Pacific Economic Co-operation (Apec) summit in Indonesia.
Libyan Prime Minister Ali Zeidan's office said he had asked for clarification on the raid and stressed Libya was "keen on prosecuting any Libyan citizen inside Libya".
"The Libyan government has been following the reports of the kidnap of one of the Libyan citizens wanted by the authorities in the United States," said a Libyan government statement issued on Sunday.
"As soon as it heard the reports, the Libyan government contacted the US authorities to demand an explanation."
Citing surveillance camera footage, Mr Liby's son, Abdullah al-Ruqai, said his father was seized in Tripoli early on Saturday by masked gunmen armed with pistols, as he was parking outside his house.
He said that those he could see taking his father looked Libyan and spoke a Libyan dialect.
He claims the Libyan government was implicated in his father's disappearance - a claim Tripoli denies.
Mr Liby's brother, Nabih, on Sunday told reporters his brother was innocent, describing the US operation as an "act of piracy".
Anas al-Liby - real name is Nazih Abdul-Hamed al-Ruqai - 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.
The 49-year-old has been indicted in a New York court in connection with the attacks.
On Saturday, US commandos also carried out a raid in southern Somalia, but failed to capture their target.
Pentagon spokesman George Little confirmed on Monday that they were chasing Abdukadir Mohamed Abdukadir, a Kenyan al-Shabab commander also known as Ikrima.
He is alleged to have been involved in plotting a number of attacks in Kenya.
Al-Shabab has said it carried out last month's attack on the Westgate shopping centre in the Kenyan capital, Nairobi.
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."
Mr 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".