The US pressed for a ceasefire in Libya during calls at the weekend to the government in Tripoli and its main backer Turkey.
President Donald Trump raised the issue with Turkish leader Recep Tayyip Erdogan on Saturday, the White House said.
"President Trump reiterated concern over worsening foreign interference in Libya and the need for rapid de-escalation,” spokesman Judd Deere said.
On Friday, US Secretary of State Mike Pompeo urged the Government of National Accord to accept a ceasefire with forces loyal to the rival administration in the east of Libya, and criticised the flow of weapons into the country despite a UN embargo.
“A ceasefire leading to a political resolution is the only option for the Libyan people,” Mr Pompeo said on Twitter after speaking to the GNA Prime Minister, Fayez Al Sarraj.
The State Department said Mr Pompeo called Mr Al Sarraj to “reiterate US opposition to the continued level of weapons and munitions being brought into the country”.
The two men “emphasised the importance of an immediate halt to the fighting and return to political dialogue”.
Mr Pompeo did not name a country, but the GNA's key military supplier is Turkey, which signed a pact with Tripoli in November.
A report last month by the International Crisis Group said that Turkey had sent at least 100 military officers, shiploads of weapons and aerial defences, and at least 2,000 pro-Turkish mercenaries from Syria to Libya.
Mr Al Sarraj’s government this week rejected an offer of a ceasefire from forces allied to the House of Representatives administration based in eastern Libya and led by Field Marshal Khalifa Haftar.
Ahmed Al Mismari, spokesman for Field Marshal Haftar’s forces, said they would withdraw up to 3 kilometres from Tripoli’s front lines in a “humanitarian gesture” for Eid Al Fitr.
The offer followed successes by GNA forces in recent weeks, including the capture of the Al Watiya airbase near Tripoli on Monday, and was dismissed by GNA Interior Minister Fathi Bashagha as an attempt to disguise a retreat.
Field Marshal Haftar said the offensive on the Libyan capital, launched in April last year, is directed at Tripoli-based extremist militias supporting the GNA.