National Forces Alliance, Faisal Krekshi, told AFP.
The alliance of liberal forces is headed by Mahmud Jibril who played a prominent role as rebel prime minister during the popular revolt that toppled Gadhafi last year.
The leader of one of Libya's main Islamist parties acknowledged that the rival coalition had the advantage in the country’s two largest cities.
“The National Forces Alliance achieved good results in some large cities except Misrata. They have a net lead in Tripoli and in Benghazi," said Mohammed Sawan, who heads the Justice and Construction party.
"But it is a tight race for us in the south," added Sawan, a former political prisoner and member of Libya's Muslim Brotherhood, which launched the party. The bulk of Libya's population and registered voters are concentrated in the capital, which lies in the west of the oil-rich desert country, and in the eastern city of Benghazi.
Libyans on Saturday voted for a General National Congress, a 200-member legislative assembly which will steer the country through a transition period. Turnout was above 60%, the electoral commission said.
A total of 80 seats in the incoming congress are reserved for political entities while the remaining 120 are held for individual candidates, some of who are openly allied to specific parties. Altogether, 3,707 candidates stood in 72 districts nationwide.
Sawan said the results were mixed in terms of which party was performing better when it comes down to allies and sympathisers who are running as individual candidates.
Votes were still being tallied by Libya's electoral commission with preliminary results expected by Monday night. The world is waiting to see whether Libya, a conservative Muslim country with no significant minorities, will deliver a win for Islamists like in Egypt and Tunisia.
Clinton pledges US support
US secretary of state Hillary Rodham Clinton is congratulating Libya for holding is first nationwide vote in decades. She says the U.S. stands ready to help the North African nation become a free and peaceful democracy.
Speaking Sunday in Japan, Clinton called the Libyan vote a "historic milestone."
She says that "after more than four decades of authoritarian rule, men and women from every corner of Libya are determining their own future"
She says it's the "will of the people, not the whim of the dictator." AP