The UN envoy for Yemen appealed to the warring parties on Tuesday to finalize a peace deal as soon as possible, saying slow progress has been made in the past two months and it's now time for concessions on the toughest issues. 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 \u00a0have 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. ALSO READ:\u00a0UN envoy says Yemen peace talks are back on track Both sides ''have demonstrated over the past weeks a true commitment to make peace, and a political wisdom in negotiations, which did not shy away from broaching sensitive and complicated issues,'' Cheikh Ahmed said. ''I am reassured by the commitment of the two delegations, but I am appealing to them to finalize these difficult negotiations and reach a comprehensive settlement as soon as possible.'' 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. The Houthis seized the capital, Sanaa, in September 2014, forcing President Abed Rabbo Mansour Hadi to flee first to the southern port city of Aden and later to Saudi Arabia. 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. Cheikh Ahmed cited credible reports from international aid organizations ''warning of a humanitarian catastrophe, should the situation not be addressed rapidly.'' According to the UN, more than 80 percent of Yemenis are in dire need of food, water and other aid. The UN envoy said high temperatures and the lack of electricity in Aden, Hodayda and elsewhere ''have exacerbated the health crisis in these areas and caused a number of preventable deaths.'' Since the beginning of 2016, he added, Yemen's economy has shrunk by more than 30 percent which is ''alarming'' given that the country imports basic commodities such as rice, wheat and medicine. Cheikh Ahmed said that in the next few days he will provide the Yemeni parties with a written proposal for the uncoming period before consultations resume after a short break for both sides to consult their leaders.