Nickolay Mladenov told the Security Council that ongoing Israeli construction in the West Bank was one of three "negative trends" that must be quickly reversed to keep the hope of an Israeli-Palestinian peace deal alive.
Violence, incitement and the Palestinian Authority's lack of control over the Hamas-ruled Gaza Strip also "severely undermine hopes for peace," Mladenov said.
"These negative trends can and must be urgently reversed in order to advance the two-state solution on the ground," he said.
The full report prepared by the quartet -- the United States, European Union, Russia and the United Nations -- is expected to be released on Friday after months of delays, mostly over of the thorny issue of settlements, diplomats said.
Its findings and recommendations are to serve as the basis for reviving the Israeli-Palestinian peace process that has been comatose since a US peace initiative collapsed in April 2014.
Mladenov said the report outlined a "reasonable set of steps" that could set Israel and the Palestinians "firmly along a navigable course towards establishing a comprehensive peace with historic implications for the entire region."
"This has not been an easy task to draft," the envoy told reporters after a closed door meeting with the council.
Not a score card
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The report "will not be a score card for assigning blame to each side," but rather the consensus view of the four quartet powers on what needs to be done to revive prospects for a two-state solution, he said.
Mladenov expressed hope that the report will set the stage "for meaningful negotiations" between Israel and the Palestinians.
A final report draft was in the hands of quartet leaders Thursday for approval before the scheduled release on Friday.
The UN envoy asked the Security Council to endorse the report recommendations in a move that would turn the document into an internationally-agreed roadmap for Israeli-Palestinian peace.
As the council discussed the new peace plan, a Palestinian attacker stabbed and killed a 13-year-old girl in her home in a Jewish settlement in the West Bank.
Israeli-Palestinian violence since October has killed at least 211 Palestinians, 33 Israelis, two Americans, an Eritrean and a Sudanese.
French Ambassador Francois Delattre said the report could help advance plans for a Paris peace conference on the Middle East later this year.
"The French initiative and the quartet report mutually reinforce each other and have a common goal to put the peace process back on track," Delattre said.
France has set up working groups that will draw up a list of incentives for both the Israelis and the Palestinians to come to the table for talks.