"We are so happy with this election festival," Abbas said after casting his ballot. "So far, it's going very well and we hope it will keep going well until the end without any troubles."
By noon hours, more than 40 percent of eligible voters cast their ballots.
Palestinians vote in east Jerusalem (Video: Reuters)
Abbas also said he is ready to resume peace talks with Israel, even if Hamas joins his government after Wednesday's vote.
"We are ready to negotiate," Abbas told Israeli reporters who were in Ramallah to cover the election. "We are partners with the Israelis. They don't have the right to choose their partner. But if they are seeking a Palestinian partner, this partner exists."
Earlier, Palestinian Prime Minister Ahmed Qureia says the ruling Fatah party is ready to "stand behind" Hamas if the Islamic movement wins Wednesday's parliamentary vote.
"I hope that the minority will accept the decisions of the majority," Qureia said after voting in the Jerusalem suburb of Abu Dis. "If Hamas wins, they will win and we will stand behind them. This is democracy and we accept the results of the elections."
Elsewhere, Hamas' top candidate, Ismail Haniya, voted in Gaza and declared "the movement would not disarm after entering Parliament."
"The Europeans and Americans are telling Hamas to choose between its weapons and the parliament," Haniya said. "There is no contradiction between the two." Meanwhile, Hamas leader in Gaza Mahmoud al-Zahar said: "We'll maintain the path of resistance to the occupation. We won't turn into a political party."
Emotional battle between Dahlan, Hamas
First reports of election violence surfaced in the afternoon, after Hamas members clashes with Fatah members and police officers in two villages near Hebron. Several people were wounded in the clashes, including one Palestinian policeman.
Earlier, several procedural complaints were registered in connection with the vote, but there were almost no gunmen near polling stations, and those who voted left their weapons outside.
Most attention in early hours of the elections focused on the Gaza Strip town of Khan Younis, where a genuine elections atmosphere could be felt Wednesday morning and thousands of voters mixed with thousands of activists belonging to the various parties and groups.
Elsewhere, the elections are proceeding calmly and without unusual incidents.
Voting in Gaza (Photo: AFP)
Khan Younis is a test case because it is also the riding of Muhammad Dahlan, considered Gaza's strongman and one of Fatah's leading figures. As a result, Hamas devoted much of its election campaign to attacks on Dahlan in a bid to prevent him from winning.
During the campaign, Dahlan and Hamas engaged in mutual mudslinging and accused one another of betraying the public's trust and embezzling public funds. Hamas members said Dahlan and his associates stole millions of dollars earmarked for aid to the PA, while Dahlan and his associates charged Hamas also stole millions of dollars, earmarked for various charity foundations.
In recent days, the elections campaign in the Palestinian Authority was conducted under the cloud of the vocal television debate between Dahlan and al-Zahar. The debate featured mostly personal insults and the trading of low blows.
Dahlan and Abbas also invested great efforts in convincing independent candidates associated with Fatah to withdraw, in order not to play into Hamas' hands. Meanwhile, dozens of yellow taxicabs bearing Dahlan's pictures could be seen throughout Khan Younis, while Hamas members used megaphones to call on voters to vote for Islam, "in favor of change, and against corruption."
Surprise at refugee camp
Elsewhere, a pleasant surprise awaited voters at the Balata refugee camp in the West Bank, where Fatah al-Aqsa Martyr's Brigades members who threatened to disrupt the elections decided to maintain the peace after all.
The group's leader in the camp, Ala Sankara, arrived at the polling station accompanied by about 30 gunmen, told security forces at the site he had a "surprise," and explained he came in peace. Sankara than handed over his weapon in order to cast his ballot.
"This is a happy day, and I'm glad I got to see the Palestinian people vote," he said. "I gave my vote to Fatah, the party we defended with our blood and will continue to do so."