Mr Abbas told the Security Council that "to solve the Palestine question.it is essential to establish a multilateral global mechanism".
Abbas said the conference should lead to full United Nations membership for the state of Palestine, mutual recognition of Israel and Palestine, and the creation of a new global mechanism to reach a final settlement.
The Palestinian president immediately left the council chamber following his address on Tuesday, leaving Israeli Ambassador Danny Danon to complain that he was once again "running away" from dialogue.
U.S. Ambassador to Israel David Friedman warned a group of Jewish American leaders that Israel could face the risk of civil war if it ever dismantled its settlements in the West Bank, Israel's Channel 10 News reported on Monday.
Katz said the rapid growth of the settlements should put to rest the idea of a two-state solution favored by the Palestinians and most of the worldwide community.
A couple from Khan Yunis, a city in the southern Gaza Strip, has named their newborn triplets "Jerusalem", "Capital" and "Palestine" in protest of US President Donald Trump's recognition in December of Jerusalem as capital of the State of Israel.
The plan also gears up for an worldwide conference to pave the ground for negotiations while committing to the two-state solution and the establishment of an independent Palestinian state with East Jerusalem as its capital, he said. "Is it for the two-state solution or the one-state solution?" he added.
Trump has accused the Palestinians of "disrespecting" the United States when Abbas refused to meet US Vice President Mike Pence during his visit to the region last month.
She set out a choice of two paths for the Palestinian leadership, between "hateful rhetoric" and "incitement to violence" or negotiation and compromise.
"You don't have to like that decision, you don't have to praise that decision", she said.
Jerusalem's status is a major issue in the Israeli-Palestinian conflict. But know this: "That decision will not change".
The other two elements of his peace plan, Abbas said, required all parties not taking any action that prejudges the outcome of the negotiations.
"We are ready to undertake the longest journeys to the farthest places in the world in order to realize our rights", he said.
Earlier this month, Trump also declined to give a timeline for releasing the United States plan for peace between the Israelis and the Palestinians, telling an Israeli newspaper that he is not convinced that either party is committed to the process.
On December 6, the President's announcement to move the U.S. embassy from Tel Aviv to Jerusalem while declaring Jerusalem as Israel's capital unleashed fury and backlash from Arab nations and the global community.
Both Israel and the Palestinians claim Jerusalem as their historic capital.