President Vladimir Putin also said he and Recep Tayyip Erdogan had agreed on the need for aid to get to the northern Syrian city of Aleppo.
The two countries have signed a deal to construct two pipelines to send Russian gas under the Black Sea to Turkey.
Ties were strained after Turkey downed a Russian military jet last year.
But speaking at a joint news conference with Mr Putin, Mr Erdogan said he was confident that the normalisation of relations would take place rapidly.
Unlike Russia, Turkey is a member of Nato, but both countries currently have uneasy relations with the West and are also facing economic challenges.
Despite the deal, differences remain between the countries.
While Russia supports Syria's President Bashar al-Assad, Turkey has called for him to be ousted and has offered support to forces fighting Syrian government troops.
On Saturday, Russia vetoed a French-drafted UN resolution calling for an end to air strikes and military flights over Aleppo.