Palestinian President Mahmoud Abbas has asked the United Nations to recognise a state for his people, however Israeli Prime Minister Benjamin Netanyahu said only direct negotiations could deliver peace.
Mr Abbas handed UN Secretary-General Ban Ki-moon a letter requesting full UN membership, which the Security Council will consider on Monday.
The United States has vowed to use its veto if it comes to a vote.
"I do not believe that anyone with a shred of conscience can reject our application for a full membership in the United Nations and our admission as an independent state," Mr Abbas told the UN General Assembly, many members of which gave him a standing ovation.
Trying to head off a clash in the Security Council, a quartet of Middle East mediators urged a return to peace talks within four weeks, "substantial progress" within six months and an agreement to be struck within a year.
The Quartet - the US, Russia, the European Union and the UN - asked Israel and the Palestinians to submit proposals on territory and security within three months.
Previous proposed timetables for negotiations, such as a one-year deadline set by former US President George W Bush in 2007 and one by President Barack Obama a year ago, have run into the sand.
Mr Abbas' statehood ploy exposes waning US influence in a region shaken by Arab revolts and shifting alliances that have pushed Israel, still militarily strong, deeper into isolation.
In their speeches, Mr Abbas and Mr Netanyahu both said they extended their hands to the other party, but each blamed their opponents for the failure of past peace efforts.
"We cannot achieve peace through UN resolutions," Mr Netanyahu said, demanding that the Palestinians recognise Israel as the Jewish state, something they reject because they say that would prejudice the rights of Palestinian refugees.
Mr Netanyahu offered to meet Mr Abbas immediately in New York, minutes after Mr Abbas said settlement activity must cease first.
Mr Abbas' statehood request reflects a loss of faith after 20 years of failed peace talks sponsored by the US, Israel's main ally, and alarm at relentless Israeli settlement expansion eating into occupied land Palestinians want for a state.
"This (settlement) policy will destroy the chances of achieving a two-state solution and ... threatens to undermine the structure of the Palestinian National Authority and even end its existence," Mr Abbas declared.
It was the first time he has spoken so starkly of the PA's possible demise, highlighting the predicament faced by a body set up as a state-in-waiting but now seen by its critics as little more than a big municipality, managing the civilian affairs of the main Palestinian cities under Israeli occupation.
Dissolution of the PA would throw responsibility for ruling all of the West Bank back to Israel as the occupying power.
Israeli and US politicians have threatened financial reprisals that could cripple the PA, the source of 150,000 jobs.
Israeli delegates stayed in the hall during Mr Abbas' speech, which was punctuated by applause, especially when he recalled his predecessor Yasser Arafat's 1974 admonition to the UN: "Do not let the olive branch fall from my hand."
In the West Bank, flags and portraits of Mr Abbas and Mr Arafat draped buildings in a Ramallah square where Palestinians watched a live broadcast of the speech.
