Palestinian Prime Minister Ahmed Qureia, who cast his ballot in the Jerusalem suburb of Abu Dis, praised the vote in 26 West Bank municipalities as "the first step toward the establishment of the Palestinian state."
Voting in an additional 600 towns and villages is expected next year.
In other developments:
Long lines formed at polling stations in the West Bank town of Jericho, with some voters complaining they had to wait for more than four hours and still had not been able to cast their ballots. Still, many said they were eager to vote in their first local election since 1976.
"It doesn't matter, one or two hours. I'm going to vote. I have been waiting for this for a long time," said farmer Nabil Abu Kattan, 48.
Thursday marked the first time Fatah and Hamas were competing at the polls. Hamas, which is pledged to Israel's destruction, boycotted the 1996 general election because it was a byproduct of interim peace deals with Israel.
Hamas is also boycotting the Jan. 9 presidential elections, but plans to field candidates in future parliamentary and local elections.
The results will point to the mood on the Palestinian street, reports Berger. A win for Fatah will indicate that Palestinians want to return to peace talks with Israel. A victory for Hamas will be seen as meaning that Palestinians want to continue with armed resistance.
Over the past three decades, Palestinian communities in the West Bank and Gaza have been run by appointed mayors, first those chosen by the Israeli military and then by the Palestinian Authority.
The late Yasser Arafat had been reluctant to allow municipal elections, fearing that Hamas, the largest opposition group, would make a strong showing. Hamas has grown in popularity during the more than four years of Israeli-Palestinian fighting, providing social services with its private schools and clinics.
The date for Thursday's elections was set before Arafat's death in November. The 26 communities chosen for the first round are Fatah strongholds, said Ali Jarbawi, former head of the Central Elections Commission.
Some 150,000 Palestinians were eligible to vote in Thursday's elections. About 800 candidates are vying for 360 municipal council positions. Some seats were reserved for women.
Elections officials said they expect more than 90 percent of eligible voters to cast ballots.
Shops and cars throughout Jericho were plastered with pictures of candidates running for one of the town's 15 council seats. Outside polling stations, small children handed out postcards listing candidates from competing slates.
At a Jericho girls' school that had been converted into a polling station, hundreds waited to vote, filing past a cartoon poster showing people how to vote and instructing them not to smoke or carry guns inside. "Voting is a right and that right is yours," the poster said.
The polls opened about half an hour late there — and at other stations in town — because the election commission was late in delivering the ballot boxes.
"Just the crush of people was totally unexpected," said Nasser Awanja, the election official in charge of the station. "Because it has been since 1976 since we have had elections, they are really fired up," he said.
Long lines snaked around polling stations in the village of Tubas in the northern West Bank, and some of the candidates handed out sandwiches and juice to waiting voters.
"I have been standing here for an hour and half with my wife who is pregnant. She can't stand for long so I took her home and now I have come back to vote," said Musharef Mahmoud, 43. He would be very angry if his wife does not get a chance to vote, he said.
Palestinian Cabinet minister Saeb Erekat met Wednesday with Israeli officials to discuss arrangements for the presidential election. Israel has said it would withdraw troops from Palestinian cities a day before the vote, for 72 hours.