A joint investigation between British and Libyan police into the murder of WPC Yvonne Fletcher has been launched, the Foreign Office has announced.
The probe, conducted under Libyan law, will be led by a senior Libyan investigating magistrate and a senior Metropolitan Police officer.
The magistrate will summon witnesses to be questioned in front of members of the British investigating team.
WPC Fletcher, 25, was shot outside the Libyan embassy in London in April 1984.
The announcement of the new investigation follows a three-day visit to Tripoli earlier this week by detectives from Scotland Yard's Anti-Terrorist Branch investigating Wpc Fletcher's death.
A spokesman for Scotland Yard said: "We view the Libyan authorities' agreement to conduct a joint investigation with ourselves as a positive development."
Wpc Fletcher was shot dead as, together with other officers, she policed a peaceful demonstration outside the Libyan People's Bureau in St James's Square on April 17, 1984.
The bullet which killed her was fired from inside the embassy and the Yard has long suspected that Libya knows the identity of the man who fired it.
But the killer is thought to have been smuggled out of Britain after the shooting, claiming diplomatic immunity.
Eleven demonstrators were also injured.
The Metropolitan Police Federation, which previously told BBC News Online relations with Libya should not resume without justice for Wpc Fletcher, said it was "reserving judgement" on the new joint investigation.
Chairman Glen Smyth said: "If the Libyan judiciary is not independent and impartial and free of interference from government then, without that reassurance, we couldn't support this move.
"We will reserve judgment until we have these reassurances."
The organisation also wanted to know if evidence gathered would be made legally admissible to courts in England and Wales, and also where any potential future trial would be heard.
He pointed out the crime had been committed on British soil, not in
Mr Smyth said he had not been officially told of the move and had found out from news organisations.
He said he was unaware of any prior consultation with the Federation.
The visit to Libya earlier this week by Met officers was arranged by Prime Minister Tony Blair when he had talks with leader Colonel Muammar Gaddafi in Tripoli on 25 March.
Despite accepting responsibility for the murder in 1999, earlier this year the Libyan prime minister Shukri Ghanem stunned the international community when he told the BBC his country did not accept guilt for either Pc Fletcher's death or the Lockerbie bombing.
He claimed the former issue was "settled".