"The security realities on the ground in Libya are growing increasingly complex and unpredictable", said Africom commander General Thomas Waldhauser.
Libya has struggled to counter unrest since the 2011 overthrow of dictator Muammar Gaddafi, leaving dozens of militia to fill the void and ally with either the GNA or a rival administration in the east backed by Haftar.
General Hifter, leader of the self-styled Libyan National Army, announced on Thursday he was deploying his forces toward Tripoli, sparking fears that the tensions could be escalating out of control as militias from the western cities of Zawiya and Misarata said they had mobilised to confront General Hifter.
The airport has not been functional since fighting in 2014 destroyed much of the facility. Libya will always be a civilian state and the army will protect it and secure the people.' he said.
The United States military said on Sunday it had pulled some of its forces out of Libya.More news: Joe Biden addresses allegations of inappropriate touching in new video
In December Haftar met Prime Minister Fayez al-Serraj from the UN-backed government at a conference but refused to attend official talks. Ahmed al-Mesmari, spokesman for Hifter's forces, said Saturday that 14 troops had been killed since the offensive began.
Fighting was underway Sunday at the global airport, some 24 kilometres from central Tripoli, after Hifter claimed to have seized the area.
The fighting was so fierce that the United Nations called for a two-hour truce so that the injured and vulnerable civilians could be evacuated. "But we are determined to hold it on time unless compelling circumstances force us not to". Pro-government militias from the nearby base of Misrata have been moving to defend Tripoli. It answers to the authorities based in eastern Libya, who are at odds with the UN-backed government.
The UN Security Council held a close-door meeting late on Friday.
Capitalising on that success, his forces in January launched a new offensive into the oil-rich desert south, ostensibly aimed at wiping out "terrorists" and criminal groups.
The LNA moved up north from on the road from former airport in the district of Khalat Furgan, coming some 11 km from the city center, a resident said, adding he could see the troops as forces loyal to the Tripoli government withdrew.
Both countries have provided support to Gen Haftar.