Yemen's conflict began in 2014 when the Huthis seized the capital Sanaa, prompting a Saudi-led coalition to intervene the following year to prop up the internationally recognised government.
The fighting has since killed hundreds of thousands of people directly or indirectly and created what the United Nations calls one of the world's worst humanitarian crises.
The negotiations since Friday in the Jordanian capital Amman are overseen by the office of the UN special envoy to Yemen and the International Committee of the Red Cross (ICRC), said Jessica Moussan, ICRC's media adviser for the Middle East.
They are meeting "together with... parties to the conflict in Yemen to address issues pertaining to negotiations on a future release operation", she told AFP.
On Friday, the UN envoy's office said the Amman talks were a follow-up to an agreement stuck by the two sides in Stockholm five years ago.
The deal called for the "release all prisoners, detainees, missing persons, arbitrarily detained and forcibly disappeared persons, and those under house arrest", held in connection with Yemen's nearly decade-long conflict, "without any exceptions or conditions".
Moussan said the ICRC was engaged with both sides to secure a prisoner swap in line with a deal agreed in Switzerland in March that saw nearly 900 prisoners freed.
That agreement came after regional powerhouses Iran and Saudi Arabia announced they were resuming ties after a seven-year rupture, in a landmark Chinese-brokered rapprochement that has shifted regional relations.
The prisoner swap was carried out over three days in April, coinciding with intensifying diplomatic to secure a long-term ceasefire.
A six-month truce brokered by the United Nations expired in October last year, but fighting has largely remained on hold.
Saudi Arabia's ambassador to Yemen, Mohammed al-Jaber, travelled to Sanaa in April as part of a plan to "stabilise" the truce.
Although no deal was struck, Jaber had told AFP the warring parties were "serious" about ending the conflict, which the United Nations says has displaced 4.5 million Yemenis internally and pushed more than two-thirds of the population into poverty.
UN special envoy Hans Grundberg told an international forum in The Hague over the past week that "the road to peace is going to be long and difficult."
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