The Turkish official said he was aware that Serbia has "good relations" with Russia, but that the ties between Serbia and Turkey "cannot be influenced by any third side."
"Turkey, too, until now had excellent relations with Russia and I hope we will return to the old days of good relations," said he.
According to Davutoglu, Serbia and Turkey are "two countries and two peoples in the same region."
"The Balkans is like a soup into which we wish to put a nice spice to make it even tastier," the Turkish prime minister had been quoted as saying.
Relations between Turkey and Serbia "will not change - and the goal of my visit is to improve them," he said.
Commenting on Vucic's statements regarding the downing of the Russian Su-24, Davutoglu said he did not consider Serbia to be a small country - but rather "a big and important one."
He then stated that the Russian plane had "violated Turkey's airspace" and was shot down for that reason.
"We were only defending our airspace," he reiterated.
According to Davutoglu, Vucic's visit to Srebrenica "demonstrated the right stance, especially when it comes to erasing bad memories from the past."
Asked to comment on Davutoglu's remark about Turkey "wanting to add spice to the Balkan soup," Vucic said he "shies away from metaphors, because they can be interpreted in various ways."
"The Balkans represents a place of conflict and turbulence for many, for us it is the most beautiful place in the world, we and our children live here, here we wish to stay. That's the most beautiful piece of land for us and for many people who have exceptional spirit, strength, and energy, that few peoples outside of the Balkans possess," he said.
Asked whether he "expected Russia's reaction" because of Davutoglu's visit to Belgrade, Vucic said it was an internal matter for Serbia and Turkey, and that he was convinced that Serbia's friends in Russia respect that.
"Good conditions"Serbia and Turkey are bound by very important, historical ties, Turkish Prime Minister Ahmet Davutoglu said in Belgrade on Monday, underlining the importance of strengthening them even further.
Addressing the media after a bilateral meeting with Serbian Prime Minister Aleksandar Vucic, Davutoglu said that the Turkish government would be glad to have with Serbia the same arrangement as with Bulgaria and Greece, concerning a top-level council.
According to Davutoglu, the aim is to increase the volume of trade between Serbia and Turkey to USD 1 billion in 2016 from USD 780 million in 2014.
The opportunities that Serbia has offered to Turkish investors are really good. I have come here with 130 business people from Turkey, although it is very hard to arrange such a meeting at the end of the year, Davutoglu said.