"If there is no further progress in removing barriers to the export of Russian fertilisers and grain, we will think about whether this deal is necessary," Lavrov told a news conference in the Turkish capital Ankara, alongside his counterpart, Mevlut Cavusoglu.
The agreement has so far allowed the export of more than 27 million tons of grain and agricultural products.
Moscow has been complaining that its side of the agreement, promising the right to export fertilizer, is not being respected.
Negotiated in July by Turkey and the United Nations, the agreement allows Ukraine - one of the world's top grain producers - to export grain through a safe corridor in the Black Sea.
It was renewed twice. When it was extended in March, Russia said it would be valid for 60 days instead of the 120 days in the original agreement.
Turkey is pushing for a 120-day extension although it acknowledges that the agreement has not been fully implemented.
"We value the continuation of the agreement which is also important in terms of reducing the global food crisis," Cavusoglu said.
There are no sanctions on Russian exports of food and fertilizers to global markets but the problems are related to the secondary sanctions imposed on shipping and insurance companies as well as banks.
"USA and England took some steps in terms of payment and insurance but we have to be fair, the problems continue", Cavusoglu said, adding that barriers remained.
-'New world order'-
Lavrov also met with President Recep Tayyip Erdogan later Friday.
NATO member Turkey, which has good ties with both Russia and Ukraine, has pushed both countries to resume peace talks after negotiations broke down last year.
Lavrov, who arrived in Ankara on Thursday, said "Any negotiation needs to be based on taking into account Russian interests, Russian concerns."
Russia has long said it was leading a struggle against the United States' dominance over the global stage, and argues the Ukraine offensive is part of that fight.
The Kremlin this week said it had no choice but to continue its more than year-long offensive in Ukraine, seeing no diplomatic solution.
Cavusoglu, whose country hosted talks between Russia and Ukraine last year, expressed "concerns that the war will escalate in spring," calling for the resumption of dialogue.