The US Embassy in Libya announced renegade General Khalifa Haftar agreed to open key oil fields and terminals as soon as Saturday, The New Arab reported.
The move could bring the possibility of a political settlement between Haftar and Libya's UN-recognised Government of National Accord (GNA), and closer to bringing an end to the bloody civil war.
However, it is not yet clear as to whether Haftar has fulfilled his promise.
Libyan tribes in the east loyal to Haftar shut down key export terminals and turned the tap off on major pipelines since the beginning of the year, in order to apply pressure to the GNA, which is based in the capital Tripoli.
Whilst no comment was offered by representatives of Haftar's Libyan Arab Armed Forces, the US Embassy said it was encouraged by "an apparent sovereign Libyan agreement" to enable Libya's National Oil Corporation to resume its "vital and apolitical work."
The US supports "a financial model that would constitute a credible guarantee that oil and gas revenues would be managed transparently and preserved for the benefit of the Libyan people," the embassy said.
"Credible safeguards will enable all Libyans to have confidence that revenues are not misappropriated." it added.
Libya was plunged into disorder after a NATO-backed uprising overthrew former anti-West leader Colonel Mummer Gaddafi.
Libya has the largest oil reserves in Africa and the ninth-biggest known reserves in the world.