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.
Negotiations between Yemen's government and rebels, locked in a devastating war for nearly four years, opened on Thursday in what UN special envoy Martin Griffiths called a "critical opportunity".
"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 UN envoy for Yemen also said the country's warring sides have agreed on a prisoner exchange as part of confidence building measures for the war-torn nation.
Griffiths said: "Today I'm also pleased to announce the signing of an agreement on the exchange of prisoners" that will allow thousands of families to be reunited.
TRT World spoke with independent expert Afrah Nasser on the issue.
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 Abd Rabbu Mansour Hadi and Yemen's Houthi rebels, linked to Riyadh's arch rival 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.