TRIPOLI, June 11 (Reuters) - European Union officials met on Monday Bulgarian nurses and a Palestinian doctor sentenced to death in Libya for infecting children with HIV and said they saw a window of opportunity for their release. Benita Ferrero-Waldner, the EU Commissioner for External Relations, flew to Libya on Sunday with German Foreign Minister Frank-Walter Steinmeier, representing the German EU presidency, to try to advance efforts to secure the release of the medics. While they held talks in Libya, U.S. President George W. Bush said during a visit to Bulgaria it was a high priority for the United States to secure the release of the nurses. Ferrero-Waldner said the medics "can rest assured that I will continue to work with all my powers to achieve their liberation -- the sooner the better". "We do see a window of opportunity for a solution and it is our intention to make sure that it doesn't close before we can use it." On Sunday, she and Steinmeier met families of some of the hundreds of children the medics are accused of infecting with HIV and the medics themselves on Monday morning. The five nurses and a Palestinian doctor were convicted in December of deliberately infecting 426 children with HIV in a trial that has hampered attempts by OPEC member Libya to restore full relations in the West. The medics say they are innocent and were tortured to make them confess. Some Western scientists say negligence and poor hospital hygiene are the real culprits and the six are scapegoats. On Sunday Saif al-Islam, a prominent son of Libyan leader Muammar Gaddafi indicated that efforts to free the six -- jailed since 1999 -- may be nearing conclusion after "positive" indications from the EU. "If the family's demands are met I think the road is open for a settlement," he said. EU officials have said they do not expect a breakthrough during the current mission, although Driss Lagha, chairman of the Association for the Families of the HIV-infected Children, has said he hoped for a deal before June 21. Libya has suggested it can free the nurses if an agreement is reached to pay compensation to the families of the children. Tripoli has demanded 10 million euros ($13 million) for the family of each infected child. Bulgaria and its allies have rejected this, saying it would be an admission of guilt, but have offered a fund for treatment for the children at European hospitals. The European Union has donated 2.5 million euros to help fund this plan.