"Encouraging progress was made at the G7 summit, which we want to build on to re-establish international unity on Libya," Salame said after talks with Tunisia's acting President Mohammed Ennaceur.
"This will enable Libyans to improve the situation in their country and allow its neighbours, including Tunisia, to benefit from its stability."
G7 leaders on Monday issued a joint statement after their three-day summit in Biarritz, which called for an international conference to pave the way for a negotiated peace process in war-torn Libya - Italy's former colony.
A nearly five-month old conflict between eastern warlord Khalifa Haftar's forces and militias loyal to the UN-backed government in Tripoli has killed over 1,000 people and injured more than 5,700. Over 100,000 people have fled their homes since Haftar began his assault on the capital in early April, according to the UN.
The battle for Tripoli has "further polarized an already fragmented political landscape," UN Secretary-General Antonio Guterres said in his latest report to the Security Council issued on Thursday by the UN mission in Libya (UNSMIL).
Libya has been in chaos since the Nato-backed ouster of late dictator Muammar Gaddafi in popular uprising in 2011. Rival administrations in Tripoli and in the east of the country, each backed by an array of armed including Islamist groups, have been vying for control of the oil-rich country and its institutions.
( With inputs from IANS )