The United States on Friday welcomed Saudi Arabia's invitation to Yemen's Iran-backed Houthis for talks in Riyadh and described it as an "important step towards peace."

Saudi Arabia invited Yemen's Houthi delegation to Riyadh to continue ceasefire talks this week. The kingdom wanted to resume joint efforts with Oman to "reach a permanent and comprehensive ceasefire in Yemen and a sustainable political solution acceptable to all Yemeni parties," Saudi Arabia's state news agency said on Thursday.

The peace initiatives have gained momentum since arch-rivals Saudi Arabia and Iran agreed to re-establish ties in a deal brokered by China in March. A permanent ceasefire in Yemen would mark a milestone in stabilizing the Middle East.

"This important step towards peace expands on a series of engagements between Saudi Arabia and the Houthis," the US State Department said on Friday.

"The talks in Riyadh follow a visit by senior US officials to Saudi Arabia, Oman, and the United Arab Emirates last week to consult with our regional partners and the Yemeni parties about a viable path toward peace."

Iran has been supporting the Houthis since the conflict flared up in 2014. Tehran has evidently delivered small and large weapons to Houthis, as well as providing training. Houthis attacked Saudi Arabia multiple times with drones and ballistic missiles.

The trip marked the first official visit by Houthi officials to the kingdom since the war broke out in Yemen in 2014, after the Iran-aligned group ousted a Saudi-backed government in Sanaa.

The group has been fighting against a Saudi-led military alliance in a conflict that has killed hundreds of thousands and left 80% of Yemen's population dependent on humanitarian aid.