In this file photo, the shadow of Huthi rebels are cast on a large representation of the Yemeni flag as they attend a demonstration in Sanaa, Yemen, on April 16, 2015. AP
The delegation of Huthis, close to Riyadh's long-time rival Tehran, flew in late on Thursday for their first public visit since a Saudi-led coalition launched a military intervention in Yemen in 2015.
Their visit, five months after hosting a Saudi team in the Yemeni capital Sanaa, is the latest hopeful sign for a war that has created one of the world's worst humanitarian crises.
"We hope that a serious discussion will take place in the interest of both peoples and that the challenges will be overcome," senior political leader Mohamed Ali al-Huthi posted on X, formerly known as Twitter, early on Friday.
"Dialogue can only take place with the... coalition, considering that the decision... of the siege and stopping it is in its hands."
Yemen was plunged into conflict when the Huthis took control of the capital Sanaa in September 2014, ousting the internationally recognised government and prompting the Saudi-led coalition to launch their offensive the following March.
Yemen's government, now operating out of the southern city of Aden, voiced support for the talks and "all initiatives aimed at bringing about a just and comprehensive peace".
"The Yemeni government welcomed the efforts... aimed at pushing the Huthi militias towards seriously responding to calls for peace and alleviating the human suffering of the Yemeni people," said a statement on its official Saba news agency.
Cooling in tensions:
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.
In May last year, commercial flights took off from Sanaa airport for the first time in six years as coalition countries reopened their airspace, and this April, nearly 900 detainees were exchanged in a confidence-building prisoner swap.
Key to the cooling in tensions has been Saudi Arabia's detente with Iran, after seven years of ruptured ties, in March, as Riyadh tries to focus on revamping its oil-reliant economy and building future prosperity.
Days after the surprise rapprochement, the prisoner exchange was sealed during talks in Switzerland. The Saudi ambassador to Yemen led a negotiating team to Sanaa the following month.
Saudi state TV Al Ekhbariya said the current talks were aimed at "finding a comprehensive political solution in Yemen".
"The kingdom is hosting a negotiating delegation representing the Yemeni Huthi component, intending to continue the discussions aimed at finding a political solution, a comprehensive ceasefire, and moving from the stage of conflicts to stability," it said.
The Huthi demands include payment of their civil servants' salaries by the displaced Yemeni government, and the launch of new destinations from Sanaa airport.