Tunis, Tunisia (CNN) -- Tunisia was the first Arab country this year to overthrow its long-ruling dictator. And it now is the first country of the Arab Spring to hold an election, one that international observers are calling remarkably free and fair.
"Yesterday they showed an Arab country can administer an election that's well run, that gives people an opportunity to choose their own destiny," Ambassador Richard Williamson, an election monitor from the International Republican Institute, said Monday. "It was an enormous victory for the Tunisian people."
Millions of Tunisians turned out Sunday to elect representatives to a new 217-seat assembly that will be charged with writing a new constitution. The National Constituent Assembly also is likely to lay down the framework for a future system of government in this North African country.
Tunisia's main election commission said final results for the vote would not be published until Tuesday afternoon. However, at least one of the major parties competing in the vote has conceded defeat.
Mahmoud Smaoui, media coordinator for Tunisia's secular PDP party, told CNN his party was projected to have come in fourth in Sunday's election. He said the PDP was soundly beaten by the moderate Islamist Ennahada party, which he believed captured first place.
During the pre-election campaign, PDP leaders staked out a fiercely secularist position while also routinely accusing Ennahada of threatening to subvert Tunisia's secular system of government. Ennahada officials responded by calling this a campaign of "fear mongering."
"We salute the beginning of the democratic process in Tunisia. We wish good luck to the majority, which is constituted mostly of the Islamist party and other allied parties," Smaoui said in a phone call with CNN. "We will not participate in the (future) government, no matter what the proposal is."
In a democracy, he said, "there is a majority in power and then a minority in opposition. ... We in the opposition will have the chance to reinforce our party."
Meanwhile, officials from Ennahada told CNN they are pleased with preliminary results.
"I think results are very good for us," said Moadh Kheriji, chief of staff to Rachid Ghanouchi, the head of Ennahada. Kheriji said he believes there is the possibility his party captured more than 35% of the vote, though he added that he was waiting for official results.
Officials from both Ennahada and the PDP told CNN they believe two other secular parties appeared to be poised to capture second and third place, Mustafa Ben Jaafar's Ettakatol and Moncef Marzouki's Congress for the Republic [CPR].
CNN could not independently confirm these conclusions. But they appeared to match the estimates of international election monitoring groups.
"It doesn't look like any party is going to be over about 35 to 40%," said the International Republican Institute's Williamson. "Coalitions will be necessary."
Politicians from all four parties -- Ennahada, Ettakatol, CPR and PDP, -- were persecuted and either exiled or banned from participating in politics under the regime of Zine El Abidine Ben Ali.
Unlike the PDP, however, Ettakatol and CPR appear to have friendly ties with Ennahada.
"We're happy that the second and third party are serious parties that never resorted to scare tactics," said Ennahada's Kheriji.
Ambassador Williamson of IRI predicted Tunisia's emerging political parties will have to overcome long legacies of opposition politics.
"No one's going to have a majority of this new constituent assembly," he said. "So they're going to have to learn collaboration and cooperation and compromise. And in Tunisia for 43 years ... none of these things existed. So its going to be a difficult and challenging period. But to be successful they've got to develop those political skills."
Mohamed Kamez Jendoubi, the head of the country's election commission, said Monday that more than 80% of the North African nation's registered voters cast ballots the previous day. Some waited three hours, in lines looping around polling stations, to have their say in what is Tunisia's first national elections since it became independent in 1956.
"It's fabulous," said Jendoubi. "There were lines (at the polling stations) in the north, south, east and west. People were well disciplined. Normally Tunisians don't wait in line."
The vote was historic not only in Tunisia, which, until January for had been ruled for 23 years by Ben Ali, but also in the region in the world. Since Ali was ousted in January -- a month after 26-year-old street vendor Muhammad Al Bouazizi set himself afire after a police officer seized his goods -- residents in several other Arab nations have similarly rallied for democratic reforms and against their leaders, many of whom have been in power for decades and allowed little dissent.
Sunday's election was a stark contrast, with voters able to choose from members of more than 60 political parties.
Jane Harman, a former U.S. congresswoman from California who now heads the Woodrow Wilson International Center for Scholars, said Tunisia deserves praise. She said she hopes its open, democratic election, like its decision to pressure its authoritarian ruler, is followed by others in the region.
"Tunisia has set a marker here, a marker for what you do from a standing start -- they had nothing going on here except two decades of autocratic, corrupt rule (until) nine months ago," Harman said Monday. "This is how you do a fair election, this is how people participate, and this is how you open it to the world to see it."
Tunisia Afrique Pressesaid 4,100,812 people registered to vote prior to the election in a country of more than 10 million. But Jendoubi said many unregistered voters -- "mostly youth and women" -- showed up Sunday for last-minute registration.