The party, led by Mahmoud Jibril, took 70.1 percent of the vote in the city of Janzour, near Tripoli, and 55.6 percent of the ballots cast in Zliten, which saw heavy fighting in last year's war, the British newspaper The Daily Telegraph reported Monday.
In Misurata, however, Jibril's party was polling less than 10 percent of the vote, with 27 percent going to a local party and the Islamist Justice and Construction Party getting 22.6 percent.
Although only about 8 percent of the 1.8 million votes cast had been counted and reported, "informal predictions of a moderate landslide may be accurate," the newspaper said.
Jibril, a former university professor in Pittsburgh and later the economy minister in Moammar Gadhafi's regime, defected early in the revolution that toppled the dictator, become the rebels' prime minister, and dealt extensively with Western governments to secure their support for the uprising, the newspaper said.
International observers praised the election process, although two people were killed in anti-voting protests.
"It is remarkable that nearly all Libyans cast their ballots free from fear or intimidation," European Union monitor Alexander Graf Lambsdorff told a press conference.