Delegates from the Iran-aligned Houthi movement and the Saudi-backed Yemeni government had arrived in Amman earlier. They will discuss the implementation of a deal agreed in U.N-led talks in Sweden in December that would allow thousands of families to be reunited.
"The meetings of the two sides with us began," a U.N. source not authorised to speak publicly told Reuters.
Western nations, some of which supply arms and intelligence to a Saudi-led coalition backing the governmnet, had pressed the two sides to agree confidence-building steps to pave the way for a wider truce and a political process to end the war, which has killed tens of thousands of people.
The deal to free prisoners was part of confidence-building measures that included a plan to withdraw from the contested port city of Hodeidah, a lifeline for millions facing famine, and place it under the control of an interim entity.
The two sides exchanged lists of some 15,000 prisoners for a swap agreed at the start of the Sweden talks and delegates said it would be conducted via the Houthi-held Sanaa airport in north Yemen and the government-held Sayun airport in the south.
The process would be overseen by the United Nations and the International Committee of the Red Cross (ICRC). The operation will require the Saudi-led coalition to guarantee that air space is secure for flights, the ICRC said.
(Reporting by Suleiman Al-Khalidi; Editing by Catherine Evans, William Maclean)