Forces aligned with Libya's internationally recognised Government of National Accord (GNA) said on Tuesday they had withdrawn from the strategic coastal city of Sirte to avoid bloodshed, after their eastern rivals rapidly entered it and took control.

Holding Sirte would be an important gain for eastern-based commander Khalifa Haftar, who since April has waged a military offensive on the capital, Tripoli, home to the GNA, to try to extend his control across the vast, mainly desert country.

Sirte is just west of important oil export terminals, also controlled by Haftar, and is strategically positioned on supply routes between eastern, western and southern Libya.

The advance of Haftar's Libyan National Army (LNA) comes as Turkey prepares to send military advisors and experts to Libya to help shore up the GNA, part of rising international involvement in Libya's conflict.

"Our forces took a decision, after studying the situation, to withdraw outside Sirte, then await orders," the Sirte Protection Force, a GNA ally, said in a statement.

"Our forces still retain their full capabilities and our withdrawal from Sire is not the end," it added.

The LNA said on Monday it had taken Sirte in a swift advance preceded by air strikes.

Sirte lies in the centre of Libya's Mediterranean coast, and has been controlled by GNA-aligned forces since they ejected Islamic State from the city with the help of US air strikes in late 2016.

The Sirte Protection Force said it had withdrawn "to save the blood of civilians and the youth of the forces" in Sirte, adding that the LNA got help from "sleeper cells" in the city of 120 000.

Many of the Sirte Protection Force were from Misrata, a city to the northwest that led the campaign against Islamic State and is a key source of military power for the GNA.

On Tuesday, an LNA military source said LNA forces clashed with Misratan forces in Abu Grain area, between Sirte an Misrata.

The Sirte Protection Force accused LNA fighters of burning homes and committing theft and looting in Sirte after entering the city on Monday. Forces loyal to Haftar denied any violations.

"These are neither our actions or the Libyan army's actions. On the contrary, we were received with cheers," an LNA spokesperson told Reuters.

Since launching a bitter campaign for Benghazi, Libya's second city, in 2014, Haftar has gradually expanded his territorial control across the north African country.

Haftar's LNA has received material and military support from countries including the United Arab Emirates, Jordan and Egypt, according UN experts and diplomats.