However, militias loyal to the UN-backed government led by Fayez al-Sarraj, are said to have repulsed an attempt by Haftar's forces to take control of a checkpoint on the coastal road west of the capital linking Tripoli to the city of Zawiya.
Pro-government forces in Tripoli confirmed that they had targeted Haftar's men with "intensive strikes".
Haftar's forces are battling for control of an area some 30 kilometers (18 miles) south of the capital near Tripoli's global airport, which was destroyed in 2014.
The foreign ministers of Russian Federation and Egypt, which have both backed the military strongman, met in Cairo on Saturday and also said there needed to be a political solution in Libya.
Ahmed al-Mesmari, spokesman for the self-styled Libyan National Army lead by General Hifter, said 14 troops were killed since General Hifter declared the offensive. The UN-backed Libyan government calls Tripoli home, whereas Haftar has amassed his power largely in the eastern and southern stretches of Libya.
Gen Haftar began his offensive four days ago and fighting on the outskirts of the capital has led some global groups to react to the deteriorating security situation.
US Africa Command, headquartered in Stuttgart, Germany, said its mission in Libya involves "military support to diplomatic missions, counterterrorism activities, enhancing partnerships and improving security across the region".
It would also put at risk upcoming peace talks between rivals brokered by the United Nations and aimed at drawing a roadmap for new elections.
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Meanwhile residents in Misrata said armed groups from the city had begun moving towards the Libyan capital, Reuters reported.
After meeting Friday with Hifter in the eastern Libyan city of Benghazi, Guterres said in a tweet that he was leaving Libya "with a heavy heart and deeply concerned".
The U.N. Security Council on Friday also called on Haftar to halt his advance on Tripoli, warning the military move was putting Libya's stability at risk.
On Thursday, Haftar launched a military campaign to recapture Tripoli from the GNA forces. "I still hope that it would be possible to avoid bloody confrontation in and around Tripoli and the United Nation will remain available to facilitate any political solution able to unify the Libyan institutions".
U.N. Secretary-General Antonio Guterres departed after meeting Haftar to try to avert full-blown civil war.
His forces clashed south of the capital Friday and Saturday with forces that back the country's unity government. "The solution can only be a political solution".
The growing worldwide pressure on Haftar came as fresh fighting flared Saturday south of Tripoli between the pro-government forces and Haftar's troops.
He returned during the revolution and he's subsequently become the most powerful military leader in a country rife with militias, allied to a rival government in the east.