BENGHAZI, Libya (Reuters) - Forces in East Libya led by Khalifa Haftar said on Thursday they will not let up in their military campaign against rival factions in the capital Tripoli, appearing to reject a call by Russia and Turkey for a ceasefire.

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A statement from Haftar’s self-styled Libyan National Army (LNA) welcomed Russia’s bid “to seek peace and stability in Libya”, but affirmed “the continuation of the efforts of the armed forces in their war against terrorist groups ... which control the capital Tripoli”.

A high-level source close to the LNA, who asked not to be identified, described the statement as a “conditional acceptance” of Russia and Turkey’s call on Wednesday for a ceasefire to start on Jan. 12.

Haftar’s forces began an offensive to take control of Tripoli in April that quickly stalled on the city’s outskirts. However, the LNA has gained an advantage in recent weeks as fighting intensified and it seized the coastal city of Sirte on Monday.

Libya has been divided into rival camps based in Tripoli and the east since 2014, each with their own set of institutions.

Haftar’s offensive upended a U.N.-led peace push and reignited a conflict that has in recent years fuelled migrant smuggling to Europe, given space to Islamist militants and disrupted oil supplies.

Both Russia and Turkey have been increasingly involved in Libya’s conflict, with Turkey backing the internationally recognised Government of National Accord (GNA) in Tripoli and the armed factions that support it. Turkey’s parliament voted last week to allow a troop deployment to the North African country.

Russia has largely backed Haftar, whilst maintaining relations with the GNA.

In recent months Russian military contractors have deployed alongside the LNA, which has also received air support from the United Arab Emirates and backing from Jordan and Egypt, according to U.N. experts and diplomats.

The GNA has said it welcomes any serious call for a return to the political process.

“The GNA urgently wants to restore peace, and until that is possible ... we will exercise our lawful right to enter into military alliances and defend our country from attack,” senior GNA adviser Mohammed Ali Abdallah said in a statement on Thursday.

The GNA “welcomes any credible ceasefire proposal, but we have a duty to protect the Libyan people” from Haftar’s offensive, he said.