Libya has renewed its demands for the Bulgarian government to pay compensation to ensure the release of five nurses detained since 1999.
President Parvanov has been to visit the nurses in Libya
The women were sentenced to death in 2004 for deliberately infecting nearly 400 children with HIV-infected blood.
Libya, which is under international pressure to resolve the dispute, wants 'diva' or blood money to be paid to the families of the children.
Bulgaria has previously rejected Libyan calls for compensation.
Libya believes the payment would satisfy Islamic law and allow the death sentence to be withdrawn.
"An agreement with the families of the children would reflect positively on the case according to Islamic law," Libya's ambassador to Britain, Mohammed al-Zaway, told the Associated Press news agency.
"The amount that the Bulgarian government agrees on with the family is not an issue for us. The important thing is the families' agreement," he added.
Six years in jail
The nurses, along with a Palestinian doctor, were detained following the outbreak at a hospital in the eastern city of Benghazi.
Of the children affected around 50 have since died.
The Libyan government has faced intense pressure from Europe and the US to free the nurses amid accusations they were wrongly convicted.
The medics say the HIV outbreak was caused by poor hygiene practices at the hospital, including the re-use of syringes.
Tripoli has so far refused to bow to the pressure and a Libyan High Court decision on whether the women can appeal their sentences has been put back until November.