Libyan leader Muammar Gaddafi said "we are sorry" for the 1984 killing of a British policewoman outside the Libyan embassy in London which led Britain to suspend ties between the two countries for years.
Yvonne Fletcher died after being hit by shots fired from the embassy during a demonstration against Gaddafi.
"She is not an enemy to us, and we are sorry all the time and (offer) our sympathy, because she was on duty, she was there to protect the Libyan embassy, but this is the problem that should be solved — but who did it?" Gaddafi said in an interview with Sky News, to be broadcast on Monday.
Britain's foreign ministry said in a statement: "We agree with him that this issue needs to be resolved.
"Libya can help in the search for answers by allowing the U.K. police to return to Libya to complete their investigations into the murder of WPC Fletcher."
Relations with Britain were only resumed 15 years later when Libya "accepted general responsibility for the actions of those within the (embassy) ... and expressed deep regret to the family" to whom it agreed to pay compensation.
Gaddafi said Britain and Libya had enjoyed good economic relations, even when diplomatic ties had been broken.
The United States in late 2003 began a process of rapprochement with Libya, after decades of estrangement, because of Tripoli's decision to abandon the pursuit of weapons of mass destruction.
Gaddafi also talked about the release of former Libyan agent Abdel Basset al-Megrahi from a Scottish prison where he had been serving a life sentence for the 1988 Lockerbie airliner bombing in which 270 people, mainly Britons and Americans, died.
Libya angered Britain and the United States over the warm public reception it gave to Megrahi, who was freed in August on compassionate grounds as he has terminal cancer.
Critics of the move accused the government of Prime Minister Gordon Brown, and the devolved Scottish administration, of freeing Megrahi to win business deals with Libya.
Gaddafi brushed off the issue saying: "It is a matter of concern for the British, Scots, Americans. We are not really concerned about it."
Double standards over nuclear weapons?
In the wide-ranging interview, Gaddafi said a future Palestinian state should be allowed nuclear weapons unless Israel, which is widely thought to have such weapons, is disarmed.
Middle Eastern countries such as Egypt, Syria and Saudi Arabia should be entitled to develop nuclear weapons as a counterbalance to Israel, he said.
Gaddafi accused the international community of double standards over the way it has handled Israel's nuclear capabilities and Iran's nuclear program, saying Libya opposed any country having atomic weapons.
Iran has repeatedly rejected calls to curb enrichment or grant unfettered U.N. inspections aimed at verifying that it is not trying to develop nuclear arms. Israel does not discuss its nuclear capabilities under an "ambiguity" policy.
"If the Israelis have the nuclear weapons and the nuclear capabilities, then it is the right of the Egyptians, the Syrians, the Saudis to have the same — even the Palestinians should have the same because their counterparts, or their opponents, have nuclear capabilities," he said. "Why not?"