Libya says it may review death sentences imposed on five Bulgarian nurses convicted of starting an Aids epidemic, which killed 40 children.
The medics were initially accused of conspiring with foreign agents
Foreign Minister Abdelraham Shalgam said that if victims were compensated, the verdicts could be "re-examined".
The five nurses and a Palestinian doctor, who was also convicted, had pleaded not guilty, and several said they confessed under torture.
The sentences, handed down in May, were widely criticised internationally.
Both the United States and the European Union attacked the verdicts.
Prosecutors argued the accused gave patients HIV in a bid to find an Aids cure.
But the six medics say the HIV outbreak at a children's hospital in Benghazi was caused by poor hygiene.
In all, 426 children were infected with HIV and at least 40 have since died.
Now Libya says that if Bulgaria pays financial compensation to the victims and helps build a hospital for Aids sufferers, the verdicts could be reconsidered.
"There are three problems at stake: the families of the children
who died of Aids, the sick children and the Bulgarian nurses," said Mr Shalgam.
"If these two steps are fulfilled then we can talk about the
third step, which is related to reversing the verdict," he added, after discussing the issue with his Bulgarian counterpart, Solomon Passy, during a meeting of Mediterranean nations held in the Netherlands.
Mr Shalgam said that he wanted the European Union to be involved in any settlement.
The EU lifted an 18-year arms embargo in October, the latest sign of improving relations with Tripoli.
EU external affairs commissioner Benita Ferrero-Waldner has said that a conclusion to the HIV affair "would also be very good for the Libyans".