Prime Minister-designate Saad Hariri pledged to work to form a new government following the June 7 elections that brought his March 14 coalition to power.
Various lawmakers had called for a unity government, though problems were expected among rival factions in Beirut.
Mohammad Raad, a lawmaker with Hezbollah's Loyalty to Resistance slate, said there were no obstacles from the opposition in forming the new government, the Daily Star, a Lebanese newspaper, reports.
"I sense progress, which can be built upon to achieve further positive steps," he said following a meeting with President Michel Suleiman.
Raad said Hezbollah was working to coordinate with Suleiman to ensure the process of forming the next government went smoothly and in the spirit of national unity.
Former President Amine Gemayel, who heads the Phalange Party in the March 14 coalition, said the June 7 victory meant Hariri could form a new government based on a majority Cabinet if opposition talks collapsed.
March 14 won a modest victory over the opposition March 7 slate in the June 7 elections.
Charlize Theron not engaged to Sean Penn 'yet'
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend