BEIRUT, Lebanon (CNN)  -- Saad Hariri, the leader of Lebanon's Sunni-dominated "March 14 coalition," claimed victory hours after the polls closed in Sunday's crucial election.



"March 14" coalition leader Saad Hariri claims victory after polls close Sunday.



Results were not expected until midday Monday.



"What happened today proved again that Lebanon is doing well," said Hariri in a televised victory speech. "The Lebanese proved again that they are holding on to their freedom and the democratic system, so congratulations to Lebanon, congratulations to freedom and to every voter who participated in this election. In this election, there is no winner or loser, democracy won today and the biggest winner is Lebanon."



Hezbollah officials did not challenge Hariri's speech. Al-Arabiya television network cited Hezbollah sources as predicting Hariri's March 14 coalition would win 70 seats, and that the Hezbollah-dominated "March 8 alliance" would win 58 seats.



The election -- with 128 seats in parliament at stake -- was crucial in determining whether the Arab nation, scarred by war and political instability, picked the coalition led by Hariri or an alliance backed by the militant group Hezbollah.  Watch Hariri's victory speech »



Turnout was high among the country's 3 million registered voters during the 12 hours that polls were open Sunday. About 50,000 troops were on the streets, but the run-up to the balloting had been free of violence.



Former U.S. President and Nobel Peace Prize Winner Jimmy Carter on Sunday said the United States should work with whichever coalition wins -- even though it considers Hezbollah, supported by both Syria and Iran, to be a terrorist organization.



Carter was in Beirut as part of more than 200 international observers monitoring the election.



Two senior Obama administration officials -- Secretary of State Hillary Clinton and Vice President Joe Biden -- have visited Lebanon in recent months, signaling concerns over a possible Hezbollah victory.



Hezbollah grew in popularity after its militant wing claimed victory over Israel after a 34-day military conflict in 2006. Since then, it has been more widely perceived by its supporters to be the "defenders" of Lebanon.



In Lebanon's unique power-sharing government, the presidency is reserved for Maronite Christians, the speaker of parliament is always a Shia Muslim, and the prime minister is a Sunni Muslim. The law was created to balance power among Lebanon's three main religious groups.



Resident Georges Azzi, who cast his ballot early Sunday morning, hoped the elections bring about a smooth and healthy transition to a new government and the continued support of the West -- whatever the results.



"I think it would be seen as a punishment to everybody if it doesn't," Azzi said. "We should accept the results whatever they are. That's how democracy works."



CNN's Cal Perry and Saad Abedine contributed to this report
Where is Carter at? Who gave a victory speech? When are results expected? What did officials not challenge? What is at stake? When are the results expected? What is Carter in Beirut part of? What did Hezbollah not challenge?
Beirut Saad Hariri, midday Monday. Hariri's speech. 128 seats in parliament midday Monday. more than 200 international observers monitoring the election. Hariri's speech.
question: Where is Carter at?, answer: Beirut | question: Who gave a victory speech?, answer: Saad Hariri, | question: When are results expected?, answer: midday Monday. | question: What did officials not challenge?, answer: Hariri's speech. | question: What is at stake?, answer: 128 seats in parliament | question: When are the results expected?, answer: midday Monday. | question: What is Carter in Beirut part of?, answer: more than 200 international observers monitoring the election. | question: What did Hezbollah not challenge?, answer: Hariri's speech.