The negotiations followed a truce proposed by Russian Federation and Turkey that began Sunday - the first break in fighting in months. He has not commented since then whether he will sign it or not.
A Greek government spokesman Stelios Petsas said at a media briefing on Tuesday that Greece was at the centre of developments in Libya and should have a place on the summit that was announced by German Chancellor Angela Merkel on Saturday.
Officials from the United States, Russia, Britain, France, China, United Arab Emirates, Turkey as well as several African and Arab countries are also invited.
Addressing his ruling party's legislators, Erdogan praised Sarraj, saying he had displayed "an extremely constructive and compromising" stance during the talks in Moscow. Putin said any Russians in the country are not in Moscow's pay. "We have completed our duty".
"We will pursue our efforts in this direction". Russia, European powers and Libya's neighbours "are working in the same vein and motivating all Libyan sides to agree rather than continue sorting things out by force", Lavrov said.
The nine-month war over Tripoli is just the latest bout of chaos in Libya, an OPEC oil exporter that has become a hub for human traffickers to ship migrants by boats to Italy, while Islamist militants have exploited the widespread disorder. "For now, a definitive result has not been achieved", Lavrov said at a press conference in Sri Lanka, according to AFP.
The Russian defence ministry was quoted by Interfax news agency as saying Haftar had been positive about the ceasefire deal and was taking two days to consider it. There were immediate reports of violations by both sides, however, raising concerns it might not hold.
Since the ousting 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. On Sunday, Germany will host a summit on Libya involving the rival camps.
Both Russia, which backs Gen Haftar, and Turkey, which supports the GNA, were behind efforts to reach a truce. The U.S. Embassy said they discussed "issues of mutual interest".
The two delegations from Libya on Monday spent seven hours in an attempt to sign a deal outlining the terms of a permanent truce in Libya, following a ceasefire that took effect over the weekend.
Turkey has said it will send military advisers and possibly troops to reinforce its support to the GNA, while Russian military contractors have been deployed alongside LNA.