Stephen Gibbs: Further frustration for relatives of those who died

The meeting, at a secret location in the desert, came at the end of a day fraught with delay and confusion.

Mr Annan said afterwards that the talks had been "fruitful and positive". He said Tripoli had confirmed it accepted the men should be tried in a foreign country.

"Libya has confirmed its seriousness and readiness to find a solution to the Lockerbie problem," he said.

"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."

Our diplomatic correspondent in Tripoli says that since a final deal was what Mr Annan went to Libya to achieve, the outcome must be regarded as a setback.

The United States Government says it is disappointed that the mission - to resolve the deadlock on the handover of two Libyans suspected of the 1988 Lockerbie bombing in which 270 people died - had not ended with Libya handing over the suspects.

State Department spokesman James Foley said: "We are disappointed that Libya is still not in compliance with the Security Council resolutions. Compliance means turnover of the two suspects for trial."

Kofi Annan speaking after his meeting with Colonel Gaddafi

The principle sticking point is thought to be the question of where the suspects would serve a sentence if they were found guilty.

Cook happy

UK Foreign Secretary Robin Cook said on Sunday he was encouraged by the talks.

Cook: No move on Scotland trial

"Kofi Annan has completed his objective which was to explain clearly to Colonel Gaddafi in person the nature of the offer and that we're serious about it - that its not a political trick.

"He assured me this morning that he has made it very clear to Colonel Gaddafi that there is no point holding out for agreement for imprisonment somewhere other than Scotland, " he told BBC One's Breakfast with Frost programme.

The BBC's World Affairs Editor in Tripoli, John Simpson, says Mr Annan has not achieved as much as he had hoped, although the gap between the two sides had lessened.

Statements in the official Libyan news agency, Jana, on Saturday reaffirmed the Libyan position that the Colonel does not have the constitutional power to make a deal but that any decision on the fate of the bombing suspects must be made by the Libyan People's Congress.

BBC's John Simpson: They did meet but failed to make a definitive agreement

In theory the People's Congress has the final say, but correspondents say it is not clear whether this is going to be used as a reason for refusal, or as a means of giving public endorsement to a risky decision by Colonel Gaddafi to agree to a trial.

Jana also announced that the Congress will begin an annual session on Tuesday.

Families look to trial

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.

Dr Jim Swire, whose daughter died in the bombing and who is founder of the support group for British victims' families, has said the planned trial must go ahead.

"Unless this trial is allowed to take place there is no way in which Libya will be able to escape the implication that she was guilty," he said.

A spokesman for the families of American victims, George Williams, was also optimistic about the prospect of a trial despite state department comments:

"Usually a world leader won't go somewhere unless he knows he's coming away with something concrete - so I believe we'll hear something in a short period of time."

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