Palestinian leader Mahmoud Abbas has submitted his request to the UN for recognition of a Palestinian state.
To rapturous applause in the General Assembly, he urged the Security Council to back a state with pre-1967 borders.
He said the Palestinians had entered negotiations with Israel with sincere intentions, but blamed the building of Jewish settlements for their failure.
Israeli PM Benjamin Netanyahu said he was reaching out to Palestinians and blamed them for refusing to negotiate.
"I continue to hope that President Abbas will be my partner in peace," he said in his speech in New York.
"Let's meet here today in the United Nations. Who's there to stop us?"
Mr Netanyahu added that the core of the conflict was not settlements but the refusal of the Palestinians to recognise Israel as a Jewish state.
Meanwhile the Quartet of Middle East mediators - the UN, EU, US and Russia - said in a statement it wanted Israelis and Palestinians to meet within one month to agree an agenda for talks, and aim for a peace deal by the end of 2012.
Hours after receiving it, UN Secretary-General Ban Ki-moon transmitted the Palestinian request to the Security Council.
Nawaf Salam, Lebanon's ambassador to the UN and the current Security Council president, said the application would be discussed on Monday.
In order to pass, it would need the backing of nine out of 15 council members, with no vetoes from the permanent members, but it could take weeks to reach a vote.
Israel and the US say a Palestinian state can only be achieved through talks with Israel - not through UN resolutions.
'Come to peace'
President Barack Obama told Mr Abbas on Thursday that the US would use its UN Security Council veto to block the move.
"I call upon the distinguished members of the Security Council to vote in favour of our full membership," Mr Abbas told the General Assembly, in what was for him an unusually impassioned speech.
He added that he hoped for swift backing. Many delegates gave him a standing ovation, and some were clapping and even whistling in support.
BBC Middle East editor Jeremy Bowen says this is significant because the Palestinians may yet apply to the General Assembly for enhanced status if their Security Council bid fails.
"I also appeal to the states that have not yet recognised the State of Palestine to do so," Mr Abbas said.
"The time has come for my courageous and proud people, after decades of displacement and colonial occupation and ceaseless suffering, to live like other peoples of the earth, free in a sovereign and independent homeland," he said.
He urged Israel to "come to peace".
And he said the building of Jewish settlements was "the primary cause for the failure of the peace process".
A spokesman for the Islamist movement Hamas, which controls the Gaza Strip, criticised the speech.
Salah Bardawil said Mr Abbas had deviated from the aspirations of the Palestinian people by accepting the 1967 borders, which he said left 80% of Palestinian land inside Israel.
'Future and destiny'
Meanwhile in the West Bank, crowds roared their approval as Mr Abbas demanded UN acceptance of a Palestinian state within pre-1967 borders.
"With our souls, with our blood, we will defend Palestine," they said.
Mr Abbas had called for peaceful marches in support of his initiative, but some clashes were reported:
- One Palestinian was shot dead by Israeli troops during clashes in the village of Qusra, south of Nablus, Palestinian sources say
- At the Qalandiya checkpoint, Israeli troops fired tear gas on stone-throwing Palestinian youths
- In the village of Nabi Saleh, protesters burned Israeli flags and pictures of President Obama
The process began with Mr Abbas presenting a written request for a State of Palestine to be admitted as a full UN member state to the UN secretary general.
The BBC's Kim Ghattas at the UN says that until the last minute, Western diplomats tried and failed to stop the Palestinians making the request.
Even now, efforts are under way to restart direct talks between the Israelis and Palestinians in an attempt to defuse tensions, our correspondent says.
Currently the Palestinians have observer status at the UN.