Russia ordered sweeping retaliatory measures after Turkish fighter jets shot down the warplane on Tuesday, threatening ties between two rival players in the Syrian war and raising fears of a wider international conflict.
After a series of furious tit-for-tat recriminations, Ankara said President Recep Tayyip Erdogan wanted to meet his Russian counterpart Vladimir Putin "face to face" when the two leaders are in Paris for the climate summit next week, although the idea has had a cool response from Russia.
Ankara has also "temporarily" suspended air strikes against IS targets in Syria in order to avoid any further such confrontations, Turkey's Hurriyet newspaper said.
Turkey says the plane strayed into its airspace and ignored repeated warnings but Russia, which has been waging air strikes in Syria since September, insisted it did not cross the border.
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"While the measures to defend our territory will remain in place, Turkey will work with Russia and our allies to calm tensions," Davutoglu wrote in today's edition of The Times in London.
Russia and Turkey are uneasy allies but are on opposite sides in the Syrian conflict, with Ankara backing rebels fighting to topple the regime of President Bashar al-Assad while Moscow is one of his last remaining allies.
The downing of the plane has highlighted the difficulty of forging consensus on Syria but Davutoglu said the world should unite against a "common enemy".
"The international community must not turn on itself. Otherwise the only victors will be Daesh... And the Syrian regime," he said, using an Arabic term for IS jihadists.
But the Kremlin said today that Western powers were not ready to form a coalition with Russia to fight the IS group.
Russia launched its own air strikes in support of the Assad regime in September, to the consternation of Western and Arab nations involved in US-led coalition bombing IS targets in both Syria and Iraq.