The group, the Revolutionary Council of Eastern Ghouta, said one hostage would die for each Syrian killed by government forces.
The hostages were kidnapped in August while on what Iran has described as a religious pilgrimage. The rebels have described the hostages as members of Iran's military, an assertion Iran has denied.
Iranian Foreign Minister Ali Akbar Salehi talked with Davutoglu by telephone Saturday and urged him to help secure release of the hostages.
The semi-official Mehr News Agency said Salehi also spoke with the prime minister of Qatar in an effort to resolve the situation.