In the wake of the November incident Moscow slapped a range of sanctions on Ankara, including an embargo on some Turkish food products, as well as a ban on charter flights and sales of package tours to the country and the reintroduction of visas for Turkish visitors.
"I want to start with the question of tourism...We are lifting the administrative restrictions in this area," Putin told government ministers in televised comments.
The breakthrough phone call by Putin to Erdogan came after the Turkish strongman on Monday sent a letter to the Kremlin leader that Moscow said contained an apology.
In a statement, the Kremlin said that Putin expressed "profound condolences" over the bombing and shooting attack at Istanbul's main airport that killed at least 41 people and was pinned by Ankara on Islamic State group.
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The Turkish presidency said in a statement that Erdogan and Putin "highlighted the importance of the normalisation of bilateral relations between Turkey and Russia."
The downing of the Russian warplane in Syria slammed the brakes on burgeoning relations between Russia and Turkey and sparked a bitter war of words between the leaders.
Putin called it a "stab in the back" and demanded an apology from Erdogan, who he also accused of being involved in the illegal oil trade with the Islamic State group.
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.
The crisis in relations severely hit Turkey's tourism industry, with the number of Russian tourists drastically declining in holiday resorts along the Mediterranean coast.