The relationship between the traditionally friendly countries hit rock bottom following last year's incident when Turkey shot down a Russian jet.
Following months of uncertainty, Turkey and Russia are moving towards normalising relations after Turkish President Recep Tayyip Erdogan wrote to his Russian counterpart emphasising on importance of improving ties.
Economic relations between the traditionally friendly countries hit rock-bottom after Turkish military shot down a Russian jet in November 2015 for violating its airspace.
Russia denied its jet had crossed over.
That incident had immediate fallout as Moscow discouraged its tourists from visiting Turkey and suspended work on an important transnational gas pipeline.
Turkey's Deputy Prime Minister Numan Kurtulmus said the thaw follows recent letters to the Russian leadership from Erdogan and Prime Minister Binali Yildirim.
"I want to once again express my sympathy and deep condolences to the family of the Russian pilot who died and I say: 'I feel a deep sadness,'" the Kremlin, in a statement, cited Erdogan as saying in the letter sent to President Vladimir Putin.
The Kremlin responded to the downing of the plane by slapping trade restrictions on Ankara.
There was no word from the Russian authorities on Monday on ending the sanctions.
If the dispute is now on the way to being resolved, that could ease some of the diplomatic tensions around the Syria conflict.
Moscow supports regime leader Bashar al-Assad while Ankara backs oppositions who are trying to oust him.
In its statement, the Kremlin said Putin had received a letter from Erdogan "in which the Turkish leader expressed his desire to resolve the situation connected to the downing of a Russian military aircraft".
"The letter states, in particular, that Russia is a friend to Turkey and a strategic partner, with which the Turkish authorities would not wish to spoil relations," the Kremlin statement said.
Turkey's efforts to mend damaged ties come as the Middle East is polarised by Syria's civil war, the rise of DAESH threatens regional security, and as its relations with Europe and the United States are strained.
The Kremlin statement said Erdogan had expressed his readiness to do everything necessary to restore the traditionally friendly relations between Turkey and Russia, and also to jointly fight terrorism.
After the Kremlin revealed the existence of Erdogan's letter, the Turkish lira firmed against the U.S. dollar.
The Kremlin's announcement came hours after Turkey and Israel said they would normalise ties after a six-year rupture, a rare rapprochement in the divided Middle East.
Days after taking office last month, Yildirim said Turkey needed to "increase its friends and decrease its enemies", in what appeared a tacit admission that his predecessor's policies had left the NATO member sidelined.
Under former Prime Minister Ahmet Davutoglu, Ankara was insistent on Assad's departure as the only way of stabilising Syria, setting it at odds with Moscow.