Voting opened across the Gaza Strip and the West Bank at 7am (0500 GMT) on Wednesday against a backdrop of massive security in place.
Initial results were expected shortly after the close of polling at 7pm (1700 GMT).
About 1.34 million residents of the West Bank, Gaza Strip and annexed East Jerusalem are entitled to cast their ballots in an election whose outcome promises to have a profound impact on the future course of the Middle East.
All Palestinian political factions, except the Islamic Jihad Movement, are participating in the elections, Aljazeera's correspondent Jivara al-Budairi said.
Al-Budairi reported that 300 Israeli settlers guarded by Israeli occupation forces were controlling the entire old part of the city.
The forces prevented some 5500 voters from casting their votes by not allowing the opening of polling stations. Some headed out of the city to cast their votes in other polling booths.
There were no incidents in Hebron. Also, Palestinian police were not allowed to enter the city to guard any of the polling stations.
There were no hurdles to voting
in Ram Allah
According to observers, there has been an unprecedented turnout of voters.
Jimmy Carter, the former US president present as an observer in the town of Bait Numer in northern Hebron, confirmed that the process was fair and going on orderly.
Hiba Akila, Aljazeera's correspondent in Gaza, reported that voting was calm and smooth.
Voters had flocked to the polling centres. Most markets remained closed and people were queuing at polling stations, the correspondent reported.
Aljazeera's bureau chief in Palestine Walid al-Umari, reporting from Ram Allah, said there had been no news of obstacles to voting in that area.
Mahmoud Abbas, the Palestinian president, cast his vote and expressed satisfaction with the progress of the electoral process. However, he referred to some difficulties due to Israeli measures in Jerusalem and at some of the checkpoints.
Some Palestinian armed men at the Balata refugee camp cast their votes after handing over their arms before entering the polling centre.
That implied that the resistance groups were abiding by the law, al-Umari said.
Members of Hamas could be seen welcoming voters into the polling stations as the doors opened in the Islamists' Gaza Strip stronghold.
In the West Bank, small queues had formed outside schools and other public buildings across the territory where voting was to take place.
Abbas has warned against
attempts to disrupt the vote
Abbas earlier told security forces to respond with an "iron fist" to anyone who attempted to disrupt the vote. All the main armed factions have pledged to ensure that the vote is carried through peacefully.
In an election-eve message to the Palestinian people, Abbas said the vote would serve as a decisive step on the path to statehood and pave the way for a new era of political pluralism and democracy.
"This great day will be of historic significance, a decisive step on the road to freedom and independence," he said.
The Palestinian leadership is well aware that a successful exercise in democracy will enhance the cause for statehood, with hundreds of international observers present to oversee the ballot.
A real threat
Fatah, the movement founded by the late Yasser Arafat more than 40 years ago, faces a real threat of losing its majority in parliament.
Polls indicate that Hamas is likely to run it a close second.
Nabil Shaath, Fatah's campaign manager and outgoing deputy prime minister, expressed confidence this week that the party would win a "large majority".
"Tomorrow's elections are an historic opportunity for the Palestinian people and a step towards their objective of reaching national independence"
Acting Prime Minister,
But an election-eve poll by the Near East Consulting Institute, based in Ram Allah, forecast Fatah would win only 59 out of the 132 seats, five more than Hamas, with the rest split between minor parties and independents.
Half the deputies will be elected on lists while the remainder will be voted for in 16 constituencies.
Hamas has been seeking to cash in on voter disillusionment with Fatah over the stalled peace process, widespread corruption and by saying its fighters forced Israel to pull out of Gaza last summer.
The possibility of a Hamas win, or strong enough showing to secure a seat in cabinet, has prompted warnings from Israel that it will not deal with a Palestinian government which includes a "terrorist organisation".
Hamas, which refuses to recognise Israel's right to exist and has been behind the majority of attacks in a five-year uprising, continues to advocate the use of violence while fielding its first parliamentary candidates.
In a speech on Tuesday, Ehud Olmert, the acting prime minister of Israel, also hailed the vote as a historic opportunity for the Palestinians to move towards their goal of independence.
But he said they must decide whether to take their destiny in hand or again let the "extremists" take control.
"Tomorrow's elections are a historic opportunity for the Palestinian people and a step towards their objective of reaching national independence," he said.