In statements issued from Tripoli, the Libyan capital, and Edinburgh, the men's legal advisers said that they would only face a court in a neutral 'third' country.
Speaking after a weekend summit meeting in Tripoli, Alistair Duff, the Edinburgh solicitor-advocate representing the men, said they wanted to stand trial to 'clear their names' and to rid their families of a 'deep sense of shame'.
After receiving legal advice, they had taken a 'clear decision that they are willing to stand trial in an alternative country, preferably an Arab-speaking one or one in the Mediterranean area.'
The two Libyans felt that it was 'unreasonable' to expect a Scottish or American jury to be be uninfluenced by 'prejudicial pre-trial publicity'.
Mr Duff added: 'If the British and US authorities refuse to accept a third country, there will be no trial ever, anywhere.'
Abdel Basset Ali Mahmed al- Megrahi and Al-Amin Khalifa Fhima, who are thought to be Libyan agents, are charged with blowing up Pan Am flight 103 over Lockerbie five years ago, killing 270 people.
Mr Duff spoke after the Lord Advocate, Scotland's senior law officer, and the Foreign Office bitterly criticised him and other members of the defence team.
Lord Rodger of Earlsferry QC described as 'nonsense' their arguments that a fair trial could not be held in Scotland and Foreign Office officials accused the team of 'prevarication'.
The news comes as the United Nations Security Council prepares to vote on increased sanctions against Libya.
Britain, France and the United States have called for tough new measures - banning the sale of oil- refining equipment and freezing overseas financial assets - after Colonel Muammar Gaddafi, the Libyan leader, failed to meet a UN- imposed deadline to hand over the men.
Libya is understood to have ruled out a handover.
The Foreign Office yesterday ruled out a trial in a third country. 'As a lawyer, Mr Duff can advise his clients in whichever way he thinks appropriate,' a spokesman said.
'But from our side the bottom line remains the same. We expect the two suspects to be handed over, or hand themselves over, for trial in Scotland or the US.'
The Crown Office in Edinburgh, Scotland's prosecution authority, repeated that it wanted the men to stand trial in Scotland.
Despite Mr Duff's comments, an English solicitor representing the men refused to rule out a Scottish trial.
Stephen Mitchell said: 'I have spent most of my professional life doing emotional cases where one side bangs its fist and says what the other side wants is impossible. Sooner or later one side gives way.'
Leading article, page 19