Liberals claimed an early lead on Sunday in vote counting across the country after Libya held its first free elections following Muammar Gaddafi's ouster, winning plaudits from the international community.
If the trend is confirmed, Libya unlike neighbouring Tunisia and Egypt whose strongmen were also toppled in last year's Arab Spring, will buck the trend of electoral success for Islamist movements.
"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, told AFP.
The alliance which groups more than 40 small parties is headed by Mahmud Jibril who played a prominent role as rebel prime minister during last year's popular revolt that toppled dictator Gaddafi and ended his four-decade rule.
The leader of one of Libya's main Islamist parties, also basing his assessment on their vote count observers, acknowledged the rival coalition had the edge 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 per cent, 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.
Sawan told AFP 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 with preliminary results expected by Monday night or early Tuesday.
But early media reports seemed to back the party leaders' claims.
Private channel Al-Assima TV said the coalition was far ahead in the capital, scooping 80 percent in the district of Tripoli Centre, and 90 percent in the impoverished district of Abu Slim.
Its lead, the channel said, was also strong 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.
Apart from acts of sabotage in restive eastern Libya and one death in Ajdabiya as unknown gunmen opened fire near a polling station, the vote was held in a festive atmosphere in the major cities.
Benghazi election commission chief Jamal Bugrien said six out of 174 polling stations in the Greater Benghazi area were affected by protests such as ballot burning.
But the overall voter turnout for the region was 67 percent, he told AFP. "Six polling stations were affected but they later reopened and overall voting in Benghazi went smoothly."
On Sunday, oil facilities in eastern Libya resumed normal operations, an industry official said, after a three-day protest over the region not being granted more seats.
"We have started work since this morning at Haruj and Al-Sidra terminals. The work is back to normal," said Milud Mohammed Ali, acting superintendent of Haruj terminal.
Leading a chorus of praise, US President Barack Obama said the vote was "another milestone" in Libya's transition to democracy.
"On behalf of the American people, I extend my congratulations to the people of Libya for another milestone on their extraordinary transition to democracy," Obama said.
"Today's historic election underscores that the future of Libya is in the hands of the Libyan people," said the US leader.
Britain's Foreign Secretary William Hague said the vote was a "landmark," while his Italian counterpart Giulio Terzi hailed a "watershed" moment for its former colony and crucial energy source.
Alexander Graf Lambsdorff, who heads a team of 21 European Union observers, said large numbers of Libyans had voted "peacefully and free of fear and intimidation."
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.