Turkey backs the UN-recognised Government of National Accord (GNA) of Fayez al-Sarraj based in Tripoli while analysts say Moscow supports Haftar, whose eastern-based forces last April launched a bid to seize the capital.
A peace conference in Berlin this month agreed a new push for peace - but without the two protagonists meeting - and Haftar also did not sign onto a ceasefire deal when both were in Moscow.
"Together with Russia - unfortunately we could not manage this with our EU partners, as with Syria - we spent some efforts and there has been a ceasefire," said Cavusoglu.
"Then we got together in Berlin and we committed there to a sustainable truce and ceasefire. Sarraj did. But Haftar did not make any announcement, as he did not sign the joint statement in Moscow."
"This is the only problem," he said. Earlier Wednesday, rocket fire targeted the Libyan capital's sole functioning airport, dealing another setback to peace efforts.
Turkey has sent troops to Libya in a deployment that has disturbed its Western allies. Cavusoglu insisted they were only limited in numbers and there for training but not to fight.