Palestinian statehood: Abbas to seek full UN membership
He said full UN status was a legitimate right for the Palestinian people. The address comes before a meeting of the UN General Assembly next week.
Mr Abbas's move sets up a confrontation with Israel, which sees the initiative as an attempt to isolate it.
Washington is also opposed, saying it will use its veto.
US officials urged the two sides to return to the negotiating table whatever happened in New York.
The Palestinian leader said he wanted recognition as a state within 1967 borders.
This includes the West Bank - including East Jerusalem - and the Gaza Strip.
All of these areas were occupied by Israel in 1967.
Israel withdrew its troops from Gaza in 2005, but is still in control of its airspace and coastline.
This speech ticked all the right boxes - dealing with Palestinian fears and Israeli criticisms. It also spelt out a clear strategy - the Palestinians will seek full membership of the UN via the Security Council, despite US opposition.
There have been questions over the effect any UN bid could have on the Palestine Liberation Organisation - and its ability to represent all Palestinians. Mr Abbas insisted its status would not be affected. He repeatedly mentioned refugees and the diaspora. At the same time Palestinians were told to keep matters peaceful and warned they were facing "a difficult mission… not a joy-ride."
Israeli arguments that the UN bid is "unilateral" and will prevent a return to negotiations on core issues were roundly dealt with.
President Abbas is not always a good public speaker but in this 30-minute address he appeared composed and relaxed, even making some humorous asides.
'Dead end'
Mr Abbas chose the bid for full membership over the less controversial option of asking the UN General Assembly to upgrade Palestinian status from observing entity to non-member.
If statehood is rejected the Palestinian Authority could still pursue this option.
Mr Abbas said more than 126 countries had now recognised Palestine as a state, and his people had run out of patience.
"Our sincere and continuing efforts to achieve through negotiations and resolution that will put an end to occupation and emerge as an independent Palestinian state has reached an impasse, a dead end," he said.
"We are going to the United Nations to request our legitimate right, obtaining full membership for Palestine in this organisation," he added.
He said that he would seek a vote on the issue in the Security Council, a move which is likely to result in a US veto.
The BBC's Jon Donnison, in Ramallah on the West Bank, says the veto could inflame Arab opinion at a time of huge upheaval in the Middle East.
But Mr Abbas also aimed to play down expectations, our correspondent says, adding that the move would not end Israel's occupation.
He urged Palestinians to remain peaceful, saying violence would harm the Palestinian cause, and he stressed the UN move was not a substitute for negotiations.
"We are not heading there to delegitimise Israel, no one can do this, it is a state with full membership at the UN," he said. "We want to delegitimise the Israeli occupation and its measures on our territories."
Financial sanctions
Israeli spokesman Mark Regev said there would be no official Israeli response to the speech.
But earlier in the day he said the Palestinian move would damage the prospects for peace, adding that the path to peace lay through direct negotiations in Ramallah and Jerusalem and not through the UN.
ick to play
Susan Rice on US opposition to the Palestinian UN bid
Israeli government ministers have threatened retaliation, including potentially damaging financial sanctions.
Israel sees the statehood initiative as an attempt to undermine its legitimacy.
Meanwhile correspondents say White House officials are still unsure what course the Palestinians would take at the UN.
"Whatever happens at the United Nations, there's going to have to be a process to get these two parties back to the table when we get beyond next week," said Deputy National Security Adviser Ben Rhodes, quoted by the Associated Press.
The Islamist movement Hamas, which controls the Gaza Strip, said Mr Abbas' move was unilateral and "carried great risks".
There has been an intense round of diplomacy focused both on the UN meeting next week and on trying to revive stalled peace talks.
US diplomats Dennis Ross and David Hale, EU foreign policy chief Catherine Ashton and Middle East envoy Tony Blair are all in the region.
Earlier on Friday, Palestinians threw stones at Israeli security forces near the West Bank village of Nabi Saleh. The Israelis fired tear gas.
There were more protests in the West Bank village of Walaje.