It said 27 donors, including 17 governments, nine private companies and one non-governmental organisation, had also pledged to contribute to the fund.
The Benghazi International Fund was created in January 2006 as an international NGO based in Libya with the objective of alleviating the suffering of the victims of the HIV infection in Benghazi the six medics were accused of spreading.
Five Bulgarian nurses and a Palestinian doctor spent more than eight years in jail after being accused of deliberately infecting more than 400 children, 50 of whom have since died.
The medics were returned to Bulgaria after a deal was reached which included medical help, political ties between the European Union and Tripoli, and compensation for the families of the victims.
The six, who had been sentenced to death, have maintained their innocence and said they were tortured into confessing.
The Bulgarian government said the debt was accumulated for arms and technical deliveries during the country's communist era.
Ivailo Kalfin, foreign minister, said $56.6m was Bulgaria's estimate of the debt - $20m plus more than $36m in interest.
"This debt has not been served for over 18 years and there is no clear agreement on its exact amount. So this is our understanding of the amount of the debt," Kalfin said.
"I hope that in additional talks between Libya and the international fund they will come to this number for the amount of the debt."