The commander's abrupt departure in the early hours of Tuesday was a setback for an worldwide diplomatic push in recent days, though Moscow insisted it would continue mediation efforts. He has also warned his country would "teach a lesson" to Haftar if he resumed his attacks on GNA forces.
On Monday, Moscow hosted talks on cease-fire agreement between the east-based Libyan National Army and the UN-backed Tripoli-based Government of National Accord.
Sarraj wanted Haftar's troops to withdraw to 4 April battle-lines, before the LNA launched an offensive on the capital Tripoli.
Turkey's defence ministry observed all sides were abiding by the ceasefire and the situation was calm except for "one or two separate incidents".
Since the ouster of late ruler Muammar Gaddafi in 2011, two seats of power have emerged in Libya: one in eastern Libya supported mainly by Egypt and the UAE, and the other in Tripoli, which enjoys United Nations and worldwide recognition.
"Today we can report that some progress was made", Lavrov told reporters at the elegant 19th century Moscow mansion where the talks were held.
President Recep Tayyip Erdogan said Turkey will not refrain from "teaching a lesson, quot; to the renegade Libyan general Khalifa Haftar if his forces continue the attacks against the internationally recognized government in Tripoli".
"I call on all Libyans to turn the page on the past, reject discord and to close ranks to move towards stability and peace", he said in a short televised speech. Erdogan said the issue would be discussed in Berlin on Sunday by European, North African and Middle Eastern countries as well as the the United Nations, the EU, the African Union and the Arab League.
A representative of the government associated with Haftar had signed the deal, providing brief optimism that the commander eventually would, too. Pro-LNA channels said Haftar had already left Moscow. "Despite this, we found that the talks in Moscow were positive as they showed the true face of the Haftar coup to the global community".
Sarraj on Monday called on Libyans to "turn the page on the past", as he prepared to sign the agreement.
Erdogan said Turkey will join Germany, Britain and Russian Federation at a summit which Chancellor Angela Merkel is to host in Berlin on Sunday to discuss Libya.
The Moscow talks come after a ceasefire, initiated by Turkey and Russian Federation, saw a lull in heavy fighting and air strikes on Sunday, though both factions accused each other of violating that truce as skirmishes continued around Tripoli.
Early Sunday the head of the GNA, Fayez Al-Sarraj, also announced his acceptance of the cease-fire, saying it had taken effect at the start of Sunday.