In the first days of April, Khalifa Haftar, commander of forces loyal to Libya's eastern government, launched a campaign to capture Tripoli, where a rival UN-recognized Government of National Accord (GNA) is headquartered.
The disclosure of the call and a U.S. statement that it "recognised Field Marshal Haftar's significant role in fighting terrorism and securing Libya's oil resources" has boosted the commander's supporters and enraged his opponents.
It also comes a day after United Nations envoy Ghassan Salame warned of "a widening conflagration" in other parts of the North African country.
More than 30,000 people have been displaced due to fighting near the Libyan capital, Tripoli, that has been raging since the beginning of the month, the World Health Organization said.
Ghassan Salame also said that global divisions had encouraged strongman Khalifa Haftar to launch his assault on Tripoli.
Powerful explosions, believed to be caused by aerial bombing, were reported early on Sunday across Tripoli's southern districts, with residents saying they saw an aircraft circling for more than 10 minutes over the city before opening fire on a southern district.
Libya has been struggling to make a democratic transition amid insecurity and chaos ever since the fall of former leader Muammar Gaddafi's regime in 2011.
The U.N. health agency says at least 34 more people have died in fighting for control of Libya's capital over the past two days, bringing the total to 254 dead so far, including civilians.
Colonel Mohamad Gnounou, another spokesman, said Tripoli-allied forces carried out seven air raids against military positions held by Haftar's LNA. Libya is split between rival governments in the east and west.
Forces loyal to Tripoli managed to push back the LNA several km (miles) in the southern Ain Zara suburb, Reuters reporters visiting the area said.
Russian Federation objects to the British-drafted resolution blaming Gen Haftar for the latest flare-up in violence when his LNA advanced to the outskirts of Tripoli earlier this month, diplomats said.
A UN resolution needs nine votes in favour and no vetoes by the five permanent members - United States, Britain, France, Russia or China - to pass.