SOFIA, June 1 (Reuters) - U.S. President George Bush said in an interview aired on Friday he hoped the five Bulgarian nurses sentenced to death for deliberately infecting hundreds of Libyan children with HIV would soon be freed.

Speaking to Bulgarian National Television ahead of his June 10-11 visit to Sofia, Bush said the United States was unwavering in its support for the release of the nurses, who have been imprisoned in Libya since 1999.

"We hope that this tragic, painful case will be solved quickly in a way that is satisfactory to the Bulgarian people," Bush said in the interview, part of which was aired in English with Bulgarian subtitles.

"We are very much committed to helping to not only support the nurses, but to free the nurses," he said.

The five nurses and a Palestinian doctor were convicted in December of deliberately infecting 426 children with HIV in a highly politicised trial that hampered Libyan attempts to restore full relations with the West.

The medics say they are innocent and were tortured to make them confess, and the United States and the European Union have stepped up pressure on Tripoli to release them.

Libya has suggested it can free the nurses if an agreement is reached to pay compensation to the families of the children.

Diplomats and officials say a deal could be reached soon after talks between Libya, the European Union, United States and Bulgaria resumed in early May.

The Gaddafi Foundation run by Saif al-Islam, the influential son of Libyan leader Muammar Gaddafi, has said that progress has been made in the talks and the case could be resolved very soon.

The six were recently acquitted in a separate case, in which Libyan police officers accused the medics of defaming them by testifying that they had tortured them to extract confessions.

The confessions were the key element in their convictions and defence lawyers are now hoping that they could win an appeal. No date for the appeal has been set.

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