In a statement issued last night, Mr Annan said: "Libya has confirmed its seriousness and readiness to find a solution to the Lockerbie problem.
"Libya has also agreed to a trial in a third country and believes that it ought to be possible to find answers to all other outstanding issues relating to this matter." However, he also added that more time was needed, though "not an inordinate amount".
It is now nearly a decade since the Pan Am plane exploded over Lockerbie, Scotland, killing 270 people.
When Mr Annan arrived in Libya yesterday, he was told Col Gaddafi was "in the desert" and the meeting finally took place in a desert tent. Earlier the state-controlled media had claimed that Col Gaddafi had no authority to hand over the suspects. This was seen as an attempt to create diplomatic room for a decision against giving them up for trial.
Libyan lawyers and Mr Annan's legal counsel have been discussing a US-British proposal to try the accused men on neutral territory in the Netherlands, according to Scottish law and using Scottish judges.
Libya has been under UN sanctions since 1992 for its refusal to hand over alleged intelligence agents Abdel Basset Ali al-Megrahi and Lamen Khalifa Fhimah, but the measures have had little effect.
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