Abbas for new UN status
The Palestinian leader has asked the UN to grant Palestinians "non-member observer state" by the end of the year.
Mahmoud Abbas told the General Assembly talks on such a status had begun, and that his eventual aim was to establish Palestine as a full member state.
Addressing the assembly later, Israeli Prime Minister Benjamin Netanyahu called for a "clear red line" to be set over Iran's nuclear programme.
The West suspects Iran is seeking build nuclear weapons. Tehran denies this.
Abbas told delegates the annual General Assembly in New York that Palestinians would continue their efforts to obtain full UN membership.
He said negotiations had begun with "regional organisations and member states" aimed at adopting a resolution making Palestine "a non-member state of the United Nations during this session".
"In our endeavour," he added, "we do not seek to delegitimise an existing state - that is Israel - but rather to assert the state that must be realised - that is Palestine."
Currently, the Palestine Liberation Organisation only has "permanent observer" status. Last year, a bid for full-member status failed because of a lack of support at the UN Security Council.
The change would allow Palestinians to participate in General Assembly debates. It would also improve their chances of joining UN agencies and the International Criminal Court.
In his speech, Netanyahu reaffirmed his country's opposition to "unilateral declaration of statehood".
Turning to Iran, the Israeli prime minister said "a clear red line" should be drawn which, if crossed, would lead to military intervention.
He said sanctions passed over the past seven years had not affected Tehran's nuclear programme.
Netanyahu said Iran should be stopped before it acquires enough enriched uranium to make a nuclear bomb.
"The hour is very late," he told delegates. "The Iranian nuclear calendar does not take time out."
He said he was convinced that faced with a "clear red line, Iran will back down".
On Tuesday, in his own address to the General Assembly, US President Barack Obama stressed the US would "do what we must" to stop Tehran acquiring nuclear arms.
But while the Obama administration has not ruled out a military option, it says sanctions and multilateral negotiations with Iran must still be given time to work.
Earlier this month, Secretary of State Hillary Clinton said the US was not prepared to commit to drawing "red lines", which Mr Netanyahu is insisting on.
On Wednesday, Iranian President Mahmoud Ahmadinejad accused Western countries of nuclear "intimidation", in a UN speech boycotted by the US and Israel.
"Continued threat by the uncivilised Zionists [Israel] to resort to military action is a clear example of this bitter reality," he told the General Assembly.
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