Under international pressure, the forces led by Libyan general Khalifa Haftar declared a "conditional" ceasefire in their offensive to take Tripoli from their rivals, the UN-backed Government of National Accord (GNA).
The truce went into effect early on Sunday, according to a spokesman for the Haftar-led Libyan National Army (LNA).
The LNA said they would maintain the truce in western parts of the country "provided that the other party abides by the ceasefire."
LNA spokesman Ahmed Mismari also warned that "any breach will be met with a harsh response."
Haftar launched the attack on Tripoli in April 2019, but his forces have so far been unable to seize control of the capital. The warlord is allied with an administration based in the east of the country and is believed to enjoy backing from France, Egypt and the United Arab Emirates. His rivals also claim Haftar's forces are boosted by Russian mercenaries.
However, the GNA government has allies of its own in the region, with Turkey recently deploying troops to Libya to bolster the UN-backed administration.
Earlier this week, Russia and Turkey called for a truce between the GNA and the eastern-based government.
Haftar's LNA initially rebuffed the call, but its latest announcement signaled an apparent change of heart.
It was not immediately clear if the GNA will comply with the declared truce. Although GNA Prime Minister Fayez Sarraj welcomed the Russian-Turkish initiative, he said that a ceasefire would depend on Haftar's withdrawal.
"The condition is the withdrawal on the part of the attacker, who does not seem willing because he has another modus operandi," he said after meeting Italian Prime Minister Giuseppe Conte in Rome on Saturday.
Conte and other EU leaders joined the push for a ceasefire in Libya as conflict threatens to draw in regional powers. The Italian prime minister called for an end to "foreign interference" in the North African country, once a colony of Italy.
Separately, EU Council chief Charles Michel met with Turkey's Recep Tayyip Erdogan for talks on Libya on Saturday, while Germany's Angela Merkel discussed the same issue during her Moscow visit on the same day.
