"We extend an honest call for a national dialogue to come all together in one coalition, under one banner... to reach a compromise, a consensus on which the constitution can be drafted and the new government can be composed," he said.
"In yesterday's elections, there was no loser and winner at all. Whoever is going to win, Libya is the real winner of those elections," said Jibril, one of the architects of the revolt that toppled Moamer Kadhafi last year.
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The remarks to journalists at his party's headquarters came hours after the leader of the rival Justice and Construction Party said that the National Forces Alliance (NFA) was trending well in the capital and Benghazi in the east.
Former rebel prime minister Jibril said that his NFA coalition, which he described as a nationalist movement comprising a broad spectrum of identities and ideologies, would abide by official results to be released by the country's electoral commission.
The NFA, Jibril added, groups more than 60 smaller parties.
He said the alliance had made no declarations about tallying results and slammed the media's use of the label "liberal" to describe his coalition, insisting that it was an inclusive rather than ideological organisation.
Earlier, local media and coalition members including its secretary general, said the NFA had an edge as votes were counted after the first free elections since Kadhafi's ouster.
Libyans on Saturday went to the polls to elect a General National Congress, a 200-member legislature made up of both party and individual members, which is tasked of steering the country for a transition period.
"Early reports show that the coalition is leading the polls in the majority of constituencies," NFA secretary general Faisal Krekshi told AFP.
Votes are still being processed in Libya and the world is waiting in suspense to see whether the North African nation's elections hand victory to Islamists or members of the Muslim Brotherhood as they did in Egypt and Tunisia.
"The leaders of other political parties should come to the talking table -- be this before or after results are announced. Libya needs everyone. It cannot be rebuilt with the effort of just one person or movement," Jibril said.
The coalition leader also vowed to reach out to representatives of the federalist movement, which boycotted and disrupted elections in the east.
US President Barack Obama led a chorus of praise for Saturday's historic vote.
"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.
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 they later reopened and overall voting went smoothly.
He put overall turnout for the region at 67 percent.
Votes were still being tallied with preliminary results expected by Monday night or early Tuesday.
