Davutoglu visited the Bosnian capital of Sarajevo to meet his counterpart Zlatko Lagumdzija.
Davutoglu said stability and the territorial integrity of the country should be preserved and political reforms should be launched with the help of immediate economic assistances.
The Turkish minister said that holding a protest is a democratic right "unless it spoils political stability and public order."
"Reoccurrence of political and religious civil tension in Bosnia will bring risk to the region, Europe and the international community," Davutoglu said.
Bosnian minister, Zlatko Lagumdzija, said: "Now, it is time for citizens to talk and for politicians to listen in silence. We should create a dialogue environment in Bosnia and Herzegovina."