Two detectives have visited Libya as part of the ongoing investigation into the murder of WPc Yvonne Fletcher.
The officers, from the Metropolitan Police's Counter Terrorism Command, flew to Tripoli where they met Libyan officials to discuss how the investigation can be taken forward in the future.
In a statement the force said: "We hope these preliminary discussions will pave the way for the MPS and Libyan authorities to work jointly to identify who was responsible for WPc Fletcher's murder in 1984."
The officers - a detective superintendent and a detective inspector - travelled to the nation's capital on Monday and returned to the UK last night.
They will remain in regular contact with WPc Fletcher's family who will be given an update about the visit, the force said.
WPc Fletcher, who was 25, was shot dead as she policed an anti-Gaddafi demonstration outside the Libyan People's Bureau in April 1984.
The bullets which killed her and injured 10 protesters came from inside the embassy.
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.
Last month Libyan prime minister Abdurrahim El-Keib today made a historic visit to the spot where the young officer was shot dead.
- More about: