U.N. special envoy to Yemen, Martin Griffiths, struck a positive note, saying in a brief statement read to reporters that the two sides were demonstrating a "positive spirit" in the talks, held at a castle in the town of Rimbo, north of Stockholm.
Yemen's four-year conflict, which has pushed the country to the brink of famine, pits the country's Shiite rebels, known as Houthis, against Yemen's internationally recognized government supported by a Saudi-led coalition. The United Nations has long led a push to resolve the conflict but past attempts at constructive talks have led nowhere.
"The two parties are engaged in a serious and constructive way in discussing the details of confidence-building measures," Griffiths said. "We hope we will achieve progress during this round of consultations."
Also speaking on Saturday, the third day of the talks, rebel delegate Abdul-Malik Al-Hajri said enough progress has been made on the airport issue that some "positive results" could be announced as early as Sunday.
"There was a wide-ranging discussion yesterday and today on the re-opening of Sanaa airport and, God willing, there will be some positive results tomorrow on a comprehensive scenario for the reopening of Sanaa airport," he told a news conference.
He gave no details except that one proposal made by the rebels was for Sanaa-bound aircraft to stop at another city in the region for inspection before they proceed to the Yemeni capital. He suggested Amman, Jordan's capital, as a candidate for an inspection stopover.
The Houthis captured Sanaa in 2014, forcing the government into exile and plunging the impoverished Arab nation into civil war. With the Houthis in control of most of the country, a Saudi-led, U.S.-backed coalition entered the war in March 2015 on the side President Abed Rabbo Mansour Hadi's government. The Houthis now control the north of the country while the government side controls the south.
The war has killed tens of thousands and made Yemen the world's worst humanitarian crisis with 22 of its 29 million people in need of aid, according to the U.N. The airport in rebel-held Sanaa has been closed since August 2016 by order of the Saudi-led coalition, leaving the rebel-held north of Yemen heavily relying on the Red Sea port of Hodeida, which is controlled by the Houthis, for delivery of much-needed humanitarian aid and fuel supplies.
The two sides have for months been locked at a stalemated fight over Hodeida. On the issue of the prisoner exchange, al-Hajri said the rebels were prepared to release all of those they hold, provided the other side reciprocates. The two sides, however, agreed on incremental releases, with 200 prisoners from each side being simultaneously released. He did not say when that would start.
U.N. officials have sought to downplay expectations from the talks in Sweden, saying they don't foresee rapid progress toward a political settlement but hope for at least minor steps that would help to address Yemen's worsening humanitarian crisis and prepare a framework for further negotiations.
Abdul-Majid al-Hanash, another Houthi delegate, emphasized the importance of arriving at such a framework. "In reality, what we came here for is to discuss the most important topics and that means agreeing on a framework for the political and security files," he told Saturday's news conference. "If put on the table, discussing these files will mean that we expect the battle and the war to end. This is the main objective."
Hendawi reported from Cairo.