"The ball is in the court of the Yemeni parties," Ismail Ould Cheikh Ahmed told the Security Council.
"What are the parties waiting for to sign a political agreement? Have they not understood that there are no winners in wars?"
The envoy has presented a roadmap to the Huthi rebels and their allies and the Yemeni government to end 18 months of war that has left nearly 7,000 dead, mostly civilians, and brought the country to its knees.
Under the plan, the Huthis would withdraw from Sanaa, Hodeida and Taez and hand over their weapons in a process carried out in parallel with the new political arrangements.
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One of the poorest countries in the Arab world, Yemen slid deeper into chaos when the Saudi-led coalition launched military operations in March 2015 in support of Yemen's President Abedrabbo Mansour Hadi.
Hadi yesterday rejected the UN peace proposal, saying it "rewards the putschists" who seized power in Sanaa, while the rebels said the roadmap had "fundamental flaws."
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