Palestinian leader Mahmoud Abbas has said any unity government negotiated with militant group Hamas would recognise Israel and renounce violence.
Mr Abbas is seeking a coalition between Fatah and Hamas
A Hamas official responded that there would be no explicit recognition but said it was prepared to agree to a 10-year truce with the Jewish state.
Mr Abbas is seeking a government which includes his Fatah movement and Hamas, which won elections in January.
Middle East peace negotiators are insisting on recognition of Israel.
Much international aid to the Palestinians was cut off when Hamas took power.
The BBC's Jon Leyne in Jerusalem says recognition of Israel is the crucial issue that has so far deadlocked negotiations over forming the government.
And with conditions steadily deteriorating in the West Bank and Gaza, our correspondent says, the question now is whether all sides want to find a compromise, a form of words, or whether this is going to be an issue continuing to block all political progress.
UN Secretary General Kofi Annan warned on Thursday that failure to resolve the Middle East conflict is damaging Security Council credibility.
Mr Abbas said he re-affirmed the historic statements of mutual recognition made by then Palestinian leader Yasser Arafat and Israeli Prime Minister Yitzhak Rabin in 1993.
"These two letters contain a reciprocal recognition between the PLO [Palestine Liberation Organisation] and Israel, reject violence and call for negotiations to reach a permanent settlement with the creation of an independent Palestinian state next to Israel," he said.
Mr Abbas said the unity government would also commit itself to imposing security and order, ending the phenomenon of multiple militias, indiscipline and chaos.
These commitments should lead to the resumption of withheld aid, Mr Abbas added.
But Ahmed Youssef, a senior adviser to Prime Minister Ismail Haniya, said Hamas would not join a unity government if recognising Israel was a condition.
"The national unity government does not recognise Israel in its political programme," he said.
"The government and the Hamas movement will be against recognising Israel. Our position to solve the crisis is a 10-year truce which will be good for stability and prosperity."
The Hamas government has rejected the 1993 agreements, leading to much of the Palestinians' international aid being cut off when they took power earlier this year.
A national reconciliation document drawn up in June as the basis for the new government calls for progress towards a Palestinian state living alongside Israel. But it does not explicitly recognise the Jewish state.
Echoing Arafat's address to the UN in 1974, Mr Abbas said this moment represented an olive branch of opportunity.
"I come to you bearing the wounds of a people who seek to live a normal life... not be victims of the cruelty of history," he said.
"I simply want tomorrow to be better than today. I want Palestine to be independent and sovereign... Do not let the olive branch fall from my hand."
His comments came as the Security Council met to discuss the Middle East conflict in an attempt to get the peace process back on track.
Mr Annan told the assembled ministers that peace between a new Palestinian state and a secure Israel remained distant and ill-defined.
"Like no other conflict, the Arab-Israeli conflict carries a powerful symbolic and emotional charge for people throughout the world," he said.
"And our continued failure to resolve this conflict calls into question the legitimacy and the effectiveness of this council itself."