File Photo: Mahdi al-Mashat (L), the chair of the Houthi s political council, meets Mohammad al-Jaber, the Saudi ambassador to Yemen, in Sanaa. Photo: Xinhua
The Houthi representatives had arrived in Riyadh on Thursday for their first public visit since a Saudi-led coalition in 2015 launched a military intervention in Yemen to prop up the internationally recognised government.
The delegation along with an Omani mediator "returned to the capital Sanaa after five days of negotiations in Riyadh", the Houthis' TV channel Al-Masirah reported.
The Gulf sultanate of Oman has regularly been involved in mediation efforts.
Several Yemeni officials and diplomats, all requesting anonymity as they were not authorised to speak to the media, also confirmed the return of the Houthi delegation.
There was no official comment from Saudi Arabia.
Ali al-Qhoom, a member of the Houthis' political council, said "there will be a new round of negotiations" but made no mention of any concrete achievements out of Riyadh in a statement posted on X, formerly Twitter.
The talks were "serious and positive", Qhoom said, expressing optimism that outstanding issues would be resolved.
Yemen was plunged into conflict when the Houthis took control of the capital in September 2014, ousting the internationally recognised government and prompting the Saudi-led coalition to launch their offensive the following March.
The Riyadh trip, five months after the rebels hosted a Saudi team in Sanaa, is the latest hopeful sign for a war that has created one of the world's worst humanitarian crises.
Yemen's fighting has left hundreds of thousands dead and forced millions from their homes, leaving three-quarters of the population dependent on aid.
However, the tide has turned in the past 18 months.
A UN-brokered ceasefire is largely holding, despite officially expiring in October, and the warring parties have made tentative steps towards peace.
Key to the cooling in tensions has been Saudi Arabia's detente with Iran in March, after seven years of ruptured ties.
The Houthi demands in negotiations include payment of their civil servants' salaries by the displaced Yemeni government, the release of prisoners and the launch of new destinations from Sanaa airport.
Observers say Saudi Arabia would like to see an end to its military involvement in Yemen, which has failed to defeat the Houthis and has weighed on the kingdom's finances and international image.
UN experts have accused all parties to the Yemen conflict of war crimes.