Kofi Annan speaking after his meeting with Colonel Gaddafi

UN officials in New York said that Mr Annan had gone to meet the Libyan leader at an unknown desert location.

On his return to Tripoli Mr Annan said: "Libya has confirmed its seriousness and readiness to find a solution to the Lockerbie problem.

Stephen Gibbs: Further frustration for relatives of those who died

"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.

"It will require some time but not an inordinate amount," Mr Annan said in a statement.

The BBC's World Affairs Editor in Tripoli, John Simpson, says Mr Annan has not achieved as much as he had hoped to although the gap between the two sides has lessened. It seems likely that further meetings will be necessary to make a breakthrough.

Troubled visit

Earlier on Saturday it appeared that the high-level meeting between Colonel Gaddafi and Mr Annan, to resolve the Lockerbie impasse was unlikely to take place.

The meeting was scheduled for Saturday afternoon at a secret location in the eastern Libyan city of Surt.

John Simpson: The gap is lessening

But Libya's official news agency, Jana, says Colonel Gaddafi was in a desert camp outside the region and that talks instead took place between Mr Annan and the Libyan foreign minister.

In the hope of still being able to meet the colonel, Mr Annan delayed his departure from Tripoli.

It now seems that the delay has proved fruitful although UN officials have been playing down any expectations of a big breakthrough in the discussions seeking a way of resolving the deadlock on the handover of two suspects in the 1988 Lockerbie bombing.

Compromise and sticking points

Two-hundred-and-seventy people died when Pan Am flight 103 was blown up over the Scottish town of Lockerbie.

Dr Jim Swire: 'confident of justice', Ashoor Shamis: 'Gaddafi is sulking...'

In August, Britain and America offered a compromise arrangement under which the Libyan suspects would be tried in the Netherlands under Scottish law before a panel of Scottish judges in return for the lifting of UN sanctions against Libya.

The last major sticking point is Libya's desire for the two men not to serve their sentences in Britain if they're convicted. But the UK Government will not move on this and the point was made by the Foreign Secretary, Robin Cook, in a phone call to the UN secretary-general as recently as Friday.

Privately, UN officials say most of the legal details have now been resolved and that arrangements are in place for the two suspects to be transported to the Netherlands if the meeting is successful.

Dr Jim Swire, whose daughter was killed in the plane crash and has been leading the case for British families, said he was very positive about Saturday's meeting.

Key facts on Lockerbie
Profile: Muammar Gaddafi, Libyan maverick
Profile: Kofi Annan, Master of diplomacy