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

On Monday, the forces of Libya's renegade general Khalifa Haftar said they have entered the city and took control of large parts.

Khaled al-Mahjoub, a spokesman of Haftar's self-styled Libyan National Army (LNA), said the fighters captured "all the districts surrounding the city", including al-Qardabiya airbase, before moving towards the city centre.

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However, on Monday, the GNA dismissed Haftar's claims as "rumours claiming gains of militias and mercenaries" supporting the LNA leader.

But on Tuesday, the Sirte Protection Force, a GNA ally, said it had retreated from the city.

"After studying the situation, our forces took a decision to withdraw outside Sirte, then await orders," the Sirte Protection Force said in a statement.

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

A Sirte Protection Force spokesman said the group had withdrawn "to save the blood of civilians and the youth of the forces" in Sirte, adding that the LNA got help from "sleeper cells" in the city of 120,000.

The spokesman also accused LNA fighters of burning homes 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 spokesman told Reuters news agency.

Holding Sirte would be an important gain for eastern-based 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.

Sirte lies in the centre of Libya's Mediterranean coast, and has been controlled by GNA-aligned forces since they ejected the Islamic State of Iraq and Levant (ISIL, also known as ISIS) from the city with the help of US air raids in late 2016.

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

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.

Last April, Haftar launched a military campaign to capture Tripoli from the GNA, but has so far failed to progress beyond the city's outskirts.

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His LNA forces have received material and military support from countries including the United Arab Emirates, Jordan and Egypt, according to United Nations experts and diplomats.

The LNA's advance comes as Turkey has started sending military advisers and experts to Libya to help shore up the GNA, part of rising international involvement in Libya's conflict.

Turkish President Recep Tayyip Erdogan said on Sunday that "there will be an operation centre [in Libya], there will be a Turkish lieutenant general leading and they will be managing the situation over there. [Turkish soldiers] are gradually moving there right now".

In response to Turkey's move, the European Union's top policy chief said the bloc must work towards achieving a ceasefire in Libya and called on Turkey not to send military experts and technical teams to the North African country.

"We asked for a ceasefire and we asked also to stop escalation and to end external interference, which has been increasing in the last days," EU foreign policy chief Josep Borrell told reporters following a meeting with British, Italian, German and French foreign ministers.

According to UN data, more than 1,000 people have been killed since the start of the operation and more than 5,000 injured.