Russia's foreign ministry said that it is still working with all parties to find an agreement, after initially saying there had been "progress" in the talks.
Turkey is beginning to send troops into Libya in support of the Government of National Accord in Tripoli, President Tayyip Erdogan said on Thursday, days before a summit in Berlin which will address the Libyan conflict.
Russian Federation and Turkey have turned into important players in Libya, joining Arab countries such as Egypt or the UAE which have filled a void left by Western powers showing little interest in the OPEC producer since 2011.
"We will push ahead with efforts in this direction; no final results have been achieved so far, " Lavrov told reporters, according to Russian media.
Italian Prime Minister Giuseppe Conte joined the swell of global pressure for a ceasefire during talks in Algiers in Thursday, officials said.
The leaders of the North African state's warring factions were in Moscow early this week at talks aimed at finalising a ceasefire orchestrated by Russian Federation and Turkey.
Erdoğan said in a televised speech from Ankara: "We will not hesitate to teach a deserved lesson to the putschist Haftar if he continues his attacks on the country's legitimate administration and our brothers in Libya".
He said the fact that Turkey is part of the ceasefire agreement is a question to be asked to Moscow not to his government or Haftar.
Over the weekend, German Chancellor Angela Merkel said Berlin later in January wanted to host another round of Libyan peace talks to build on the efforts by Turkey and Russian Federation.
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Monday's talks were expected to have formalised a tentative ceasefire that went into effect on Sunday.
Moscow and Ankara earlier this month announced a joint ceasefire effort, paving the way for the two powers to become peace brokers in future negotiations over Libya.
The oil-rich country has been divided since 2014 into rival camps based in Tripoli and the east, each with its own set of institutions.
Since Haftar's forces launched an offensive in Tripoli in April there have been global efforts to try to contain the crisis.
Libya plunged into chaos in 2011 after dictator Moammar Gadhafi launched a brutal crackdown against anti-government protesters.
The deal was signed by Fayez al-Serraj, leader of the GNA which has struggled to defend itself against an offensive by the LNA.
Turkey's parliament voted this month to allow a troop deployment to help the Tripoli government to fend off Haftar, who is backed by the United Arab Emirates, Egypt, Jordan and Russian mercenaries.
Haftar's LNA took control of Sirte, a strategically important city in the center of Libya's Mediterranean coastline, in a rapid advance on Monday and is seeking to consolidate gains.