The 58,700 security personnel, who will be permitted to vote through Monday, are being deployed on Wednesday, the election day, to prevent possible political violence.
Walid al-Umari, Aljazeera's Palestine bureau chief, reporting from Ram Allah said: "The process is going on very well. It aims to dedicate all security elements on the elections day for maintaining security, guarding electoral centres and preventing any problems that may obstruct the voting process.
"No trouble is expected to take place during the voting process of the security elements."
The ruling Fatah Party faces a stiff challenge from the Islamic group Hamas, which is participating in a legislative vote for the first time. A poll released on Friday put the two movements in a dead heat.
Although the two sides have pledged to avoid violence on election day, tensions remain high. Gunmen, mostly from groups affiliated with Fatah, have repeatedly taken over election and government offices in recent weeks and threatened to disrupt the election.
At the Shawki school, one of Gaza City's two polling stations, about 10 people waited quietly outside for voting to start. The school was heavily guarded, and the voters, wearing civilian clothes, had to present identification and hand over their weapons to the guards before casting their ballots.
"I came to vote because it's a national duty," said Hisham Sakallah, 39, a member of the elite Force 17 security unit. "I hope the election will pass smoothly so we can send a civilized image to the world about our people and about our respect for democracy."
Local human rights groups are
monitoring the voting
Paralyzed by disease, Sakallah, who now has an administrative job, entered the station on crutches.
"We have had no problems so far and it looks like it's a positive thing," said Hanna Nasser, head of the Palestinian election commission.
To prevent fraud, forces guarding the stations were not permitted to enter the voting areas, and each voter had to mark his finger with special ink to make sure they did not vote twice. Observers from local human rights groups monitored the voting.
Sakallah, a longtime Fatah activist, said he voted for the party because he believes it is best positioned to lead the Palestinians to independence. "They are the people who
started this process, and the people able to continue this."
Outside the station, a small group of Hamas activists wearing the group's trademark green baseball caps and bandanas greeted voters. There were no Fatah activists visible.
In the West Bank city of Nablus, dozens of police eagerly lined up at one station in the West Bank city of Nablus to vote. In Ramallah, security men wearing uniforms and green berets cast ballots quietly and orderly.
The voting was marred by accusations of wrongdoing. Hamas has accused some security commanders of ordering their troops to back Fatah - a charge denied by Palestinian officials.
"No one can know who you voted for, only God"
Some Fatah officials, meanwhile, have said that Hamas plans to punish or fire members of the security forces if it wins the election.
Hamas's No. 1 candidate, Ismail Haniyeh, urged voters "not to listen or pay attention to the rumours." In a statement issued on Saturday, the group urged security personnel "to practice their legal right to vote freely and honestly away from any form of threat."
"No one can know who you voted for, only God," the statement said.
Palestinians will choose 132 parliament members - 66 from national party lists and 66 in local district voting.
Hamas is expected to make a strong showing. Best known for carrying out dozens of bombings in Israel, Hamas has run a well-organized campaign focusing on internal Palestinian issues, such as improving public services and ending government corruption.
In contrast, Fatah has been riven by disarray, infighting and widespread perceptions of corruption.
Abbas hopes Hamas will tone
down its position after the polls
During the election campaign, Hamas candidates have generally adopted a conciliatory tone and been evasive about whether the group would renounce violence.
But at a large rally Friday, Haniyeh made clear that Hamas remains committed to destroying Israel and capturing the al-Aqsa Mosque in Jerusalem, the third-holiest site in Islam.
Palestinian leader Mahmoud Abbas has said he hopes Hamas will moderate its positions once it joins parliament or even the Palestinian government.
The acting Israeli prime minister, Ehud Olmert, planned to meet senior ministers on Sunday to discuss the state of the Palestinian Authority, Israel Radio said.
Olmert is expected to demand that Abbas disarm Hamas and other resistance groups following the election, the report said.
Olmert took over as acting prime minister this month following the 4 January stroke of Ariel Sharon, who remains unconscious in a Jerusalem hospital.