A statement from the Turkish presidency said Erdogan and Putin “highlighted the importance of the normalisation of bilateral relations between Turkey and Russia.”
The November incident froze relations between the two nations and saw Moscow slap sanctions on Ankara.
Putin also condemned the “heinous” attack at Istanbul’s Ataturk airport Tuesday that killed at least 41 people and offered condolences to the Turkish people, the statement said.
“Reiterating their commitment to reinvigorate bilateral relations and fight terrorism together, the two leaders agreed to remain in contact and meet in person,” Erdogan’s office said.
The Kremlin confirmed that the conversation took place and said a statement would be released.
The breakthrough phone call by Putin came after Erdogan on Monday sent a letter to the Kremlin leader that Moscow said contained an apology.
The downing of the plane in November ruptured relations and saw Moscow impose a raft of sanctions, including an embargo on Turkish food products and a ban on charter flights and the sale of package tours to the country.
It also sparked a bitter war of words between the leaders with Putin calling it a “stab in the back” and demanding an apology from Erdogan.
Ankara has said Erdogan expressed his “regret” over the incident in Monday’s letter to Putin and asked the family of the pilot who died to “excuse us”, but has not explicitly confirmed he apologised for shooting down the plane.
Kremlin spokesman Dmitry Peskov on Tuesday described the letter as an “important step” but warned that “there is no need to think that in several days it will be possible to normalise everything.”
Turkey has argued that the Russian plane strayed into its airspace and ignored repeated warnings, but Russia insisted it did not cross the border and accused Turkey of a “planned provocation.”
The countries are on opposing sides in the Syrian conflict, with Ankara backing rebels fighting to topple President Bashar al-Assad while Moscow is one of his last remaining allies.
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An Oxford University study established that highly religious people and atheists are the least afraid of death.