Palestinian President Mahmoud Abbas has asked the United Nations to recognise a state for his people.
But Israeli Prime Minister Benjamin Netanyahu said UN resolutions could not deliver peace.
On Friday Abbas handed UN Secretary-General Ban Ki-moon a letter requesting full UN membership, which the Security Council must consider, although this may take some time.
"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," Abbas told the UN General Assembly, which gave him a standing ovation.
"We extend our hands to the Israeli government and the Israeli people for peacemaking," the Palestinian leader said in New York.
Soon afterwards, Netanyahu followed him to the podium to argue that only direct negotiations can bring peace, a stance backed by US President Barack Obama earlier this week.
"I extend my hand to the Palestinian people," Netanyahu told the 193-nation assembly. "The truth is that Israel wants peace, the truth is that I want peace." However, he added, "we cannot achieve peace through UN resolutions".
Netanyahu also demanded that the Palestinians recognise Israel as a Jewish state, something they reject because they say that would prejudice the rights of Palestinian refugees.
Abbas's statehood request reflects a loss of faith after 20 years of failed peace talks sponsored by the United States, Israel's main ally, and alarm at relentless Israeli settlement expansion eating into the land Palestinians want for a state.
swissinfo.ch and agencies