A Metropolitan Police team is to fly to Libya to continue an investigation into the murder of WPC Yvonne Fletcher, David Cameron said on Thursday.
The visit was described as a "really positive step forward" in the inquiry into the 1984 killing of the officer, who was shot dead as she policed an anti-Gaddafi demonstration outside the Libyan People's Bureau in London.
He was speaking as the north African state's interim Prime Minister Abdurrahim El-Keib visited 10 Downing Street.
Mr El-Keib promised that his country would "work very closely together" with the UK to resolve outstanding questions about the killing of 25-year-old Wpc Fletcher, who is believed to have been hit by a shot fired from within the People's Bureau.
Her death led to an 11-day siege of the building in St James's Square and the severing of diplomatic links between the UK and Libya.
Mr El-Keib worked with the opposition while in exile during Muammar Gaddafi's dictatorship, and said he knew some of those involved in the demonstration.
He told Mr Cameron: "The Fletcher case is a case that is close to my heart personally. I had friends who were demonstrating that day next to the embassy.
"It is a sad story. It is very unfortunate that it has anything to do with the Libyan people.
"I am here to tell you that we will work very closely together to resolve anything related to that issue."
David Cameron met with Libya's interim Prime Minister Abdurrahim El-Keib. Cameron described the trip to Libya as a "really positive step forward"
Hopes of finding the killer of WPC Fletcher were raised following the revolution which toppled Gaddafi last year.
But so far, plans to send a police team to Libya have been frustrated by a failure to secure approval from local authorities.
Mr Cameron told the Libyan premier: "I am absolutely delighted that we are working so closely together on issues of mutual interest, including having a Metropolitan Police team going to Libya to continue the investigation into the murder of Wpc Yvonne Fletcher.
"I think that is a really positive step forward and I know it will be welcomed by everyone in Britain."
Officers from New Scotland Yard and Home Office Minister James Brokenshire met Mr El-Keib today to discuss the Fletcher case.
Commander Richard Walton, head of the Met's Counter Terrorism Command welcomed the invitation to visit Libya and discuss taking the inquiry further forward with authorities there.
Mr Walton said: "We have never lost our resolve to solve this murder and achieve justice for Yvonne's family. We see today's announcement as significant."
Detectives remain in regular contact with Wpc Fletcher's family and update them on developments.
Mr El-Keib said Libya wanted to be "long-term friends and partners" with Britain, and paid tribute to the role which the UK played in the international military mission to protect civilians from Gaddafi's forces during last year's uprising.
"I am here bringing with me all the sincere appreciation of the Libyan people to the UK people and you personally," he told Mr Cameron.
"You took a bold decision when it was very difficult for many to even consider supporting the Libyan people. You took that decision which inspired many of us."
Mr Cameron said: "I am very proud of the role that Britain played to help secure a successful outcome in Libya and the support we gave through the Nato mission.
"I am very much looking forward to hearing about the progress towards a full democracy in Libya and the elections which you hope to hold before Ramadan this year.
"There are huge challenges for your country - challenges we want to help you with. We really believe in the Arab Spring and what you achieved in Libya. We will be backing you every step of the way.
"(There are) big challenges like trying to integrate the revolutionary groups into the police and other armed services. We stand with you in your battle to achieve the freedom, democracy and rights that the people in Libya have wanted for so long."
The interim Libyan Prime Minister said the case was "close to his heart"
Mr El-Keib was appointed interim prime minister of Libya in October last year. Elections for a national assembly for Libya are expected in June or July, though no date has yet been set.
Mr Cameron and Mr El-Keib were also thought to be discussing the reconstruction of the country following last year's revolution.
And just days after the death of the only person convicted of the Lockerbie bombing, Abdelbaset al-Megrahi, they may also discuss whether any further evidence relating to the atrocity has emerged in the wake of the downfall of the Gaddafi regime.
Mr El-Keib spent much of his life working abroad as an academic and businessman in the United States and UAE, and played no part in Gaddafi's administration.
Downing Street later revealed that Mr El-Keib met Lord Advocate Frank Mulholland, the Scottish Government's senior legal officer, during his visit to discuss the investigation into the bombing of Pan-Am flight 103 above Lockerbie in 1988.
The only person ever convicted of involvement in the atrocity, Libyan agent Abdelbaset al-Megrahi, died last weekend.
Mr Cameron told Mr El-Keib that he hoped progress would be made on outstanding questions about Lockerbie, said Downing Street.
And the Prime Minister also raised the issue of the Gaddafi regime's support for IRA terrorism.
Characterising the talks as "warm and open", Downing Street said Mr Cameron told the Libyan PM he was "enthusiastic" about the country's future but acknowledged that challenges remained.
Mr El-Keib said progress was being made on registering voters for the upcoming elections to Libya's National Assembly, and pointed to recent local elections in Benghazi which had been conducted peacefully. Mr Cameron said he looked forward to the elections - which are due to be held before the start of Ramadan on July 20 -taking place on time.
The Libyan PM told Mr Cameron that work was "well under way" to reintegrate or demobilise all militias, and they discussed how Britain can help Libya deal with security challenges and co-operate on issues including health and higher education.
Mr El-Keib also said he looked forward to welcoming British businesses to Libya.
And he offered assurances that all those who have been detained by the Libyan authorities would receive a fair trial in an open process.