The Bulgarian government has rejected Libyan demands for "blood money" in order to secure the release of five nurses held 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.
Bulgaria believes that to pay any money would be to accept the women's guilt - something it has refused to do.
However, it has hinted at offering humanitarian assistance to the children in an attempt to resolve the situation.
Foreign Minister Ivailo Kalfin said he was ready to "assist in solving the humanitarian problem" but would not pay blood money, according to the Associated Press news agency.
"The payment of indemnity to the families is a humanitarian matter that I by no means link with any guilt of the Bulgarian medical workers in Libya," added.
Mr Kalfin said he expected to announce fresh measures to deal with the problem with the help of both the US and European governments.
"I don't want to raise false expectations, but we will think of what more can be done," he told Reuters news agency.
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, about 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.
Experts, including Luc Montagnier, a co-discoverer of the virus, say the Aids epidemic broke out because of poor hygiene at the Benghazi hospital where the incident took place.
They also say the infection spread before the nurses' arrival at the hospital.
Despite the US and others condemning the convictions, Tripoli has so far refused to bow to pressure, and a Libyan High Court decision on whether the women can appeal their sentences has been put back until November.