"Since the Oslo agreements in 1993, all these agreements are based on land and on peace and an end to Israel occupation of 1967.
"We've pledged with Israel to reach a two-state solution but month after month we've seen nothing but complacency and procrastination."
Al Jazeera's Nour Odeh, reporting from Ramallah, said Abbas's decision would have "serious implications on Palestinian politics [and] also the prospect of peace and stability in the region".
She said reactions were pouring in from followers of Abbas's Fatah movement.
"They're beginning to speak ... and we understand they're planning to march to the president's office and express their support," our correspondent said.
Abbas criticised the US for "favouring" Israel but said the Israeli-Palestinian peace process is "still possible and achievable", adding that the US can play a "central and pivotal role" to achieve peace.
His decision not to take part in the elections comes days after Hillary Clinton, the US secretary of state, visited Israel to try to kickstart the Israeli-Palestinian peace process which has stalled over Israel's refusal to halt settlement activity in the occupied territories.
Clinton said on Thursday she looked forward to working with Abbas in "any new capacity".
Speaking to Al Jazeera, PJ Crowley, spokesman for the US state department, said Washington would continue to push for a peace agreement, although he also acknowledged that the US and the Palestinian president have had their disagreements over illegal Israeli settlements and the conditions for peace talks.
"We certainly will continue our efforts and we certainly would encourage president Abbas to continue his lifelong efforts in pursuit of peace and a resolution that would lead to a Palestinian state," Crowley said.
"We still think that's possible and we're going to search for a variety of ways to get that."
Al Jazeera's Jacky Rowland, reporting from Jerusalem, said Israel was not expected to immediately react to Abbas's decision.
"The official position of the Israeli side is that this is an internal Palestinian matter and, therefore, Israel won't be making any comment at all," our correspondent said.
"But in a way it really takes the heat off Binyamin Netanyahu [the Israeli prime minister]. Afterall, it was only under a week ago that the US secretary of state was here again supposedly trying to act as some kind of intermediary to get the whole peace process moving again.
"And very much it's been a position of Netanyahu that Israel has been ready to talk; it's been the Palestinians standing in the way of talks although that might be rather a disingenuous argument. Now he [Netanyahu] can say, 'Look, we're ready to talk but there's no partner on the Palestinian side'. So it really does take the heat off the Israelis."
"This is a serious announcement saying 'I quit, I leave it to the rest'. This is a game changer for Palestinian politics and the peace process"
Marwan Bishara, Al Jazeera's senior political analyst
Al Jazeera's Zeina Awad reporting from Gaza said the Hamas leadership in the territory considers Abbas' decision as an internal matter for Fatah and the PLO, and that the actual problem was their lack of support for the principles of resistance.
She said a Hamas official told Al Jazeera that Hamas was not happy specifically with the position Abbas and his party had taken with regards "Palestinian reconciliation, and the negotiation track that they have chosen in dealing with the Israelis and achieving the two-state solution".
Saeb Erakat, the chief Palestinian negotiator, said: "At the end of the day it's not the presidency. It's the question of the Israeli government continuing settlement activity, fait accompli policies, dictation.
"And nineteen years after trying to achive a two-state solution, maybe the president has come to his moment of truth..."
Marwan Bishara, Al Jazeera's senior political analyst, said Abbas's announcement was "a game changer for Palestinian politics and the peace process".
Middle East analysts said Abbas would find it hard to make strategic concessions.
Mouin Rabbani, a contributing editor to The Middle East Report, told Al Jazeera: "After the fiascos he [Abbas] created by meeting Netanyahu and Obama in New York without any of the conditions for negotiations being met; and even more importantly after orchestrating the withdrawal of the Goldstone report from the UN Human Rights Council, he simply is not in a position to make any more strategic concessions without paying a price."
|Fatah supporters protested in Ramallah against Abbas's decision[AFP]
Abbas recenty issued a decree announcing presidential and parliamentary polls, but the Hamas-run interior ministry in the Gaza Strip ordered Palestinians not to take part in the elections.
The interior ministry said in a statement the election had been called "by figures who do not have the right to declare it".
Abbas has of late been facing heavy criticism for defending a decision to delay the endorsement of a UN report on Gaza war crimes at the UN Human Rights Council.
Although the council later passed a resolution adopting the report, Abbas continues to be criticised by Hamas, a rival Palestinian faction in control of the Gaza Strip, which has called on Palestinians to reject his leadership.
The rift between Fatah and Hamas has derailed a unity deal the two factions have been pushing forward under the auspices of the Egyptian government.
After the storm that was generated by the October 2 delay of the vote on the Gaza war report, Hamas said it had asked Egypt's intelligence chief to put off the reconciliation deal until November.