"We hope that this encounter will set the right tone for the normalisation of relations," Lavrov was quoted as saying by TASS news agency at the start of their meeting on the sidelines of a regional economic cooperation conference in the Black Sea resort of Sochi.
Encounter comes after Moscow yesterday ended a ban on the sale of package tours to Turkey in the first step to ending broader sanctions slapped on Ankara after it shot down a Russian fighter jet on the Turkish-Syria border in November.
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".
Kremlin spokesman Dmitry Peskov said today's talks were expected to help pave the way for a meeting between Putin and Erdogan that could take place either before or at a G20 summit in China in September.
Putin has now ordered his government to hold talks on lifting an embargo imposed on some Turkish food and to restore full trade ties with Ankara.
The crisis in relations with Moscow had dealt a blow to Turkish tourism, with the number of Russian tourists drastically declining in holiday resorts along the Mediterranean coast.