Ismail Ould Cheikh Ahmed told the UN Security Council that the opposing parties Houthi Shiite rebels and their allied troops loyal to a former president and Yemen's internationally recognized government have responded positively to a proposed roadmap he presented to end the conflict.
But Cheikh Ahmed said by video link from Kuwait where the talks have been taking place that the two sides have not yet agreed on the timeline and sequencing of the steps in the roadmap including when a national unity government would be created.
France's UN Ambassador Francois Delattre said the talks are at "a critical juncture" and the parties need to engage seriously and "show flexibility to find a durable peace." He warned that every passing day with more war "makes terrorist groups" such as the Islamic State and al-Qaida, stronger.
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A Saudi-led military coalition launched a large-scale airstrike campaign in March 2015 and later began on-the-ground military operations to retake rebel positions.
The US backed coalition has had success in driving the rebels out of some southern cities but has so far been unable to dislodge them from the capital and other strongholds in the north.
The conflict has killed some 9,000 people since March 2015 a third of them civilians, according to the United Nations.