Palestinians held their first presidential election in nine years Sunday, choosing a successor to longtime leader Yasser Arafat.
Mahmoud Abbas won 66 percent of the vote in the Palestinian presidential election Sunday, according to an exit poll.
Such a margin of victory would give Abbas a clear mandate to renew peace talks with Israel, rein in militants and reform the corruption-riddled Palestinian Authority.
Abbas' main challenger, Mustafa Barghouti, won 19.7 percent of the vote, according to the poll conducted by the independent Palestinian Center for Policy and Survey Research.
Sunday's voting occurred with only one known incident of violence. Five Palestinian gunmen burst into election offices, firing into the air, saying they were upset that some of their relatives' names had been left off voter registration lists in the West Bank, preventing them from participating.
Palestinian official Tayeb Abdel Rahim spoke to the men, and they left the office. No injuries were reported.
Israelis and Arabs are hoping the election will bring peace, reports CBS News Correspondent Howard Arenstein.
Israel said it is ready to meet with Abbas after the election, offering to release Palestinian prisoners if he can halt Palestinian rocket attacks.
Polls opened at 7 a.m. (midnight EST), with 1.8 million Palestinians in the West Bank, Gaza Strip and east Jerusalem eligible to vote, though an election official said the actual number of eligible voters may be lower due to outdated registration lists. The polls closed at 9 p.m. (2 p.m. EST).
Voters trickled into stations early Sunday, and activity picked up in many areas by midmorning.
Voting went smoothly in most areas, although international observers complained of confusion at Jerusalem voting stations. Police broke up two small demonstrations by Israeli extremists trying to disrupt voting in the city.
Palestinian police officer Mohammed Juma was one of the first voters at the Jalil school in Gaza City. He turned his pistol in at the entrance before casting his vote for Abbas, who is widely known as Abu Mazen.
"I believe he is the only one capable of taking us to the safe side of this ocean of conflict," he said.
"The election is going well and that indicates that the Palestinian people are heading toward democracy." He added that Israeli "obstacles exist, but our people's will is stronger than any obstacle."
According to opinion polls, Abbas holds a clear lead over his leading challenger, democracy activist Mustafa Barghouti. Five other candidates are running.
Analysts cautioned, however, that Abbas would need a strong showing — perhaps up to two-thirds of the vote — to be able to effectively deal with both militants and Israel. Recent polls forecast Abbas winning anywhere from 52 percent to 65 percent support.
Abbas has made it clear that his fundamental goal is the same as Arafat's: an end to Israeli occupation and a Palestinian state in the West Bank and Gaza Strip, with Jerusalem as its capital. He also hopes to reform his government.
He faces a difficult balancing act. He is likely to face resistance from within the corruption-riddled Palestinian Authority and from militants intent on continuing their attacks against Israel.
On the other hand, Abbas is under heavy pressure from Israel to crack down on the militants.
"After the elections, we want to see ... a strategic decision to fight the terror and incitement," Israeli Foreign Minister Silvan Shalom told Israel Radio.
Abbas has so far resisted calls for a crackdown. Instead, he hopes to persuade militants to halt their attacks on Israel.
Part of that task will involve dealing with the Islamic group Hamas, which boycotted Sunday's election. Others militants are affiliated with Fatah, but operate with great autonomy in local areas.
Zakariye Zubeydi, a senior gunman from a refugee camp in the West Bank town of Jenin, showed up with 15 armed militants from the pro-Fatah Al Aqsa Martyrs' Brigades to vote at a school. "I voted for Abu Mazen," he said.
An Israeli release of Palestinian prisoners — a top priority for Abbas — would give him a boost in his dealings with militants.
Israel holds an estimated 7,000 Palestinian prisoners. It released 159 prisoners last month, but Palestinians dismissed the gesture as insufficient.
Israeli officials, speaking on condition of anonymity, said prisoners would be released after the vote but declined to say how many.
But they said progress would depend on Abbas' ability to stop Palestinian militants firing mortar fire and Qassam rockets from the Gaza Strip.
The Israeli army eased travel restrictions and took other measures in Palestinian areas to facilitate Sunday's election. Hundreds of international observers from Europe, Japan and the United States were also on hand, including Carter and former French premier Michel Rocard.
Only minor problems were reported in Gaza and the West Bank such as an Israeli failure to remove boulders from a road leading to a polling station near Nablus. But in Jerusalem, international observers complained the vote was disorganized, and Palestinians accused Israel of trying to intimidate them.
Jerusalem is at the heart of the Israeli-Palestinian conflict, and both peoples claim it as their capital. Many Palestinians in the holy city said they would refrain from voting out of fear of jeopardizing their fragile status under Israeli rule.
"I wanted to do my part in resisting the occupation," said Jumana Khoury, a 19-year-old voter in Jerusalem, adding that having to vote in an Israeli post office was "intimidating."
Jerusalem police chief Ilan Franco ordered a heavy police presence in Arab neighborhoods, concerned that Jewish extremists would try to disrupt the vote.