The clashes between the GNA forces and Haftar's Libyan National Army (LNA) on Saturday morning came after nearly a month of calm.
LNA forces launched a surprise offensive in early April to attempt to take control of the capital Tripoli, where U.N.-backed Prime Minister Fayez Seraj and his GNA are based.
"Three fighters allied to GNA from Misrata were killed in the offensive in Tripoli this morning," the witness from the coastal city, some 200 km (124 miles) east of Tripoli, told Reuters.
An LNA military source said the offensive was repelled and the LNA maintained its positions.
The source added five LNA troops were injured. Neither side claimed significant advances.
The GNA forces' media office, Volcano Wrath, posted a photo online of heavy artillery targeting the LNA in Wadi Rabea, Qew Triangle and Sabea in Tripoli's southern suburbs.OPEC member Libya has been in turmoil since the rule of leader Muammar Gaddafi was brought to an end in a NATO-backed uprising in 2011.