With results slowly trickling in, the Tunisian electoral commission said the Ennahda party has so far won 15 out of 39 domestic seats.
Together with the results already announced from Tunisians living abroad, the party has won 24 out of 57 seats determined, or just over 42 percent.
The secularist Congress for the Republic party is a distant second so far with just 10 seats.
The moderate Islamist party does not appear to have won enough votes to control an outright majority in the 217-seat assembly, which will sit for one year to draft a new constitution and appoint a new interim president and government to run the country until fresh elections in late 2012 or early 2013.
Ennahda supporters have been celebrating on the streets of the Tunis by singing Tunisia's national anthem.
'Very Enthusiastic' Vote
An estimated 90 percent of the country's 4.1 million registered voters participated, and EU election observer mission chief Michael Gahler said operations at 97 percent of the observed polling stations had been "assessed positively."
Peru's former President Alejandro Toledo, who served as an election observer in Tunis, says voters were "very enthusiastic."
"People were very emotional," he said. And I think that whatever the results, [whatever] the final result might show, there is already one winner. Democracy has won."
Toledo also said the effect of the elections will be good not only for Tunisia but for the entire world, as people in other Arab uprising countries carry out their own votes in the months and years ahead.
"This election will have a multiplier effect on what happens in other countries such as Libya, Egypt, Syria, Yemen, and maybe other countries. Let me tell you that the organizers, the electoral board, have done an extraordinary job."
U.S. State Department spokeswoman Victoria Nuland also welcomed the vote in Tunisia as a milestone for democracy in the Arab world.
"This is obviously a significant milestone for Tunisia and for the people of Tunisia as they chart their path away from the autocratic dictatorship of the past to a government founded on respect for the will of their citizens," she said.
Outside the offices of the commission which organized the election, about 50 people staged a sit-in protest to demand an investigation into what they said were irregularities committed by Ennahda.
Election officials dismissed the protest, saying any problems during the vote were minor.
Meriam Othmani, a 28-year-old woman journalist at that protest, expressed concerns that women's rights in Tunisia will be eroded by Islamists. She also predicted that there would be a return of dictatorship in Tunisia if Ennahda is able to build a majority coalition in the constituent assembly.
But political analysts say the voting system has built-in checks and balances which make it nearly impossible for that to happen. They say Ennahda will be forced to seek alliances with secularist parties, which will dilute its influence.
Ennahda is led by Rachid Ghannouchi, a softly spoken scholar who was forced into exile in Britain for 22 years because of harassment by the former regime.
Ghannouchi dresses in suits and open-necked shirts, while his wife and daughter wear the hijab. But he says his party will not try to impose Shari'a law on Tunisian society or enforce any code of morality on the millions of Western tourists who holiday on Tunisia's beaches.
Ghannouchi says he models his approach on the moderate Islamism of Turkish Prime Minister Recep Tayyip Erdogan.
U.S. To Wait And See
The highest-profile secularist challenger to Ennahda, the Progressive Democratic Party, had campaigned by warning voters that modern, liberal values would be threatened if the Islamists won.
U.S. State Department spokeswoman Nuland said Washington would wait and see whether Shari'a law would be a factor in Tunisia's new constitution.
"The term has broad application and is understood differently in different places and by different commentators," Nuland said. "Our concern is that constitutions of new and emerging democracies -- constitutions of democracies around the world -- meet international standards of human rights."
Ennahda's preferred coalition partners may reassure some opponents of Shari'a law.
Ali Larayd, a member of the Ennahda's executive committee, said the party is ready to form an alliance with the Congress for the Republic and Ettakatol -- both secularist groups that are respected by Tunisia's secular intelligentsia.
The Congress for the Republic is led by Moncef Marzouki, a doctor and human rights activist who spent years in exile in France. Ettakatol is a socialist party led by Mustafa Ben Jaafar, another doctor and a veteran opponent of the former regime.
compiled from agency reports