"I have told our brethren in the PLO [Palestine Liberation Organisation] ... that I have no desire to run in the forthcoming election," Abbas said on Thursday in a speech broadcast live from his headquarters in the West Bank city of Ramallah.
"This decision is not a kind of compromise or a manoeuvre."
The 74-year-old leader who replaced Yasser Arafat five years ago as the Palestinian president said: "We're at cross roads. We have made lots of sacrifices in order to be able to have a right to a state.
"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.