"During the coming days we will have a critical opportunity to give momentum to the peace process," Griffiths told reporters as the rival delegations gathered in Sweden.
"There is a way we can resolve the conflict," Griffiths said, adding that the Security Council was "united" in its support for a resolution to the conflict.
"It will be done if there is a will to be make it happen."
The talks mark the first attempt in two years to broker an end to the Yemen conflict, which has killed at least 10,000 people since 2015 and triggered what the UN calls the world's worst humanitarian crisis.
Some 14 million people are at risk of mass starvation in Yemen, according to the UN, as war, a failed economy and disease bring the Arab world's poorest states to its knees.
Talks between the Saudi-backed government of Abedrabbo Mansour Hadi and Yemen's Huthi rebels, linked to Riyadh's archrival Iran, have been months in the making, with the UN sending its special envoy to Sanaa to personally escort the delegation to Sweden.
They are slated to last for one week, according to a source in the UN.
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