Leaders from Libya's warring factions were said to be travelling for talks abroad on Wednesday as reported air strikes south of the capital threatened to escalate the conflict further.
After weeks of fighting around Tripoli supported by competing foreign powers, the United Nations said on Monday that both sides had agreed to resume ceasefire talks.
However, the UN has warned that a flood of weapons and fighters into Libya in defiance of an arms embargo could fuel more fighting.
The oil-rich country has been in turmoil since 2011, when a civil war toppled long-time dictator Moammar Gadhafi, who was later killed. Libya has since split between the rival administrations in the east and the west.
The UAE and Egypt back the Libyan National Army (LNA) lead by commander Khalifa Haftar, based in eastern Libya, which are trying to take the capital Tripoli.
Turkey, backs Libya's UN recognised government in Tripoli.
PM of the Government of National Accord (GNA), Fayez al-Serraj is expected in Ankara late on Wednesday, Turkish broadcasters reported.
His deputy Ahmed Maiteeg and GNA Foreign Minister Mohamed Siyala had earlier arrived in Moscow, local media said.
"That the legitimate government has the upper hand now should be viewed as an opportunity for a political solution," Turkish Foreign Minister Mevlut Cavusoglu said in a TV interview.
Meanwhile Haftar travelled to Egypt to meet defence officials, a source close to him said.
Last week the United States said Russia had flown at least 14 warplanes to an LNA airbase in central Libya. Russia and the LNA have denied that, with the LNA saying it has refurbished some old Libyan air force jets.
The air battle has been critical, with Turkish drones knocking out LNA air defence systems and supply routes.
On Wednesday, an LNA military source said warplanes had struck near Gharyan, a town taken by the GNA last year.
It would represent the first acknowledged use of warplanes by eastern forces since Washington said Russia had supplied the MiG 29 and Su-24 jets.