"The talks today were positive and productive... It is an encouraging beginning," Ismail Ould Cheikh Ahmed told a news conference after the first direct talks since the delayed negotiations began on April 21.
"Today, we heard the parties pledge total commitment to (UN Security Council) Resolution 2216 and related decisions, the Gulf initiative and results of Yemeni national dialogue as the basis for a peaceful solution," he said.
Saturday's talks came after the government and rebel delegations each submitted a framework for a political and security solution to end the 13-month war.
Most of the meetings in talks have so far been confined to encounters between rival delegations and Ould Cheikh Ahmed.
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More than 6,800 people have been killed and around 2.8 million displaced in Yemen since a Saudi-led coalition began operations in March 2015 against Iran-backed Huthi rebels, who seized swathes of territory including the capital Sanaa.
Key issues include the withdrawal of armed groups, a handover of heavy weapons, the resumption of a political transition and the release of prisoners.