Liberals claimed an early lead on Sunday in counting of votes across the country after Libya's first free elections following the ouster of leader Moamer Gathafi.
"Early reports show that the coalition is leading the polls in the majority of constituencies," the secretary general of the National Forces Alliance, Faisal Krekshi, said.
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 Gathafi 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 percent, 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 at the polls 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 neighbouring Egypt and Tunisia.
From the parties, the National Forces coalition and two Islamist contenders, Justice and Construction and Al-Wattan, stood out from the start.
But early reports by local media seemed to back the party leaders' claims.
Private channel Al-Assima TV reported overnight that the coalition was well ahead in the capital, scooping 80 percent in the district of Tripoli Centre, and 90 percent in the impoverished district of Abu Slim.
Its edge, the channel said, was also sharp in the troubled east, with preliminary figures giving it 70 percent in Benghazi and 80 percent in Al-Bayda, hometown of Libya's interim leader Mustafa Abdel Jalil.
These figures, however, were unofficial.
"The first winner is the Libyan people," declared a beaming Nuri Abbar, head of the electoral commission, at the end of a rollercoaster voting day which was briefly clouded by unrest in the east of the country.
Alexander Graf Lambsdorff, who heads a team of 21 European Union observers, said large numbers voted "peacefully and free of fear and intimidation, despite some disturbances in the east and some tensions in the south."
"The election, however, is far from over. Counting, tallying and the publication of results are the other important steps in this electoral process," Lambsdorff cautioned.
The make-up of the congress being elected has been a matter of heated debate, with factions such as the federalist movement in the east calling for more seats and staging acts of sabotage both before and during the elections.
The outgoing National Transitional Council (NTC) says seats were distributed according to demographics, with 100 going to the west, 60 to the east and 40 to the south.
Libya has not seen national elections since the era of the late King Idris, whom Gathafi deposed in a bloodless coup in 1969.
Political parties were banned as an act of treason during Gathafi's iron-fisted rule. On Saturday, 142 parties fielded candidates.