US President Donald Trump and Egyptian President Abdel Fattah El Sisi have agreed in a phone call that they reject "foreign exploitation" in Libya and urged parties to the conflict to take "urgent steps" to resolve the fighting, the White House said.
It comes after Turkey said it will send troops to Libya at the request of Tripoli as soon as next month.
Libya's internationally recognised Government of National Accord (GNA) in Tripoli has been in conflict with Field Marshal Khalifa Haftar's forces.
An official in Tripoli confirmed a formal request had been made for Turkish military support in the air, on the ground and at sea.
The official, who asked not to be named, spoke after the GNA's interior minister, Fathi Bashagha, suggested in comments to reporters in Tunis that no such request had been made.
However an adviser to the Turkish President appeared to confirm the news.
"Libya's government has requested Turkey's military support. As President Erdogan said, we will of course honour our agreement," Fahrettin Altun tweeted
Field Marshal Haftar's fighters have made small gains in recent weeks in some southern suburbs of the capital.
Last month, Ankara signed two separate accords with the GNA, led by Fayez Al Serraj, one on security and military cooperation and another on maritime boundaries in the eastern Mediterranean.
The maritime deal ends Turkey's isolation in the East Mediterranean as it ramps up offshore energy exploration that has alarmed Greece and some other neighbours. The military deal would preserve its lone ally in the region, Tripoli.
"Since there is an invitation (from Libya) right now, we will accept it," Mr Erdogan told members of his AK Party in a speech. "We will put the bill on sending troops to Libya on the agenda as soon as parliament opens."
The legislation would pass around January 8-9, he said, opening the door to deployment.