The Yemeni government and Iran-aligned Houthis have both committed to steps toward a cease-fire, the U.N. special envoy for Yemen said Saturday.

The Houthis, which control north Yemen, have been fighting against a Saudi-led military alliance since 2015 in a conflict that has killed hundreds of thousands and left 80% of Yemen's population dependent on humanitarian aid.

The U.N. special envoy, Hans Grundberg, in a statement issued by his office said he "welcomes the parties” commitment to a set of measures to implement a nationwide cease-fire, improve living conditions in Yemen, and engage in preparations for the resumption of an inclusive political process under U.N. auspices."

Grundberg "will now engage with the parties to establish a roadmap under U.N. auspices that includes these commitments and supports their implementation," the statement said.

The roadmap, along with a cease-fire, will also include the two sides' commitment to resume oil exports, pay all public sector salaries, open roads in Taiz and other parts of Yemen, and "further ease restrictions on Sanaa Airport and the Hudaydah port," the statement said.

The Saudi-led military coalition intervened more than eight years ago against the Houthi movement after it ousted Yemen's internationally recognized, Saudi-backed government from Sanaa, the capital, in 2014.

The Saudi-backed government's foreign ministry welcomed the special envoy's statement on "the efforts made to reach a road map under the auspices of the United Nations to end the war caused by the Houthi militia," Yemeni state news agency SABA reported.

The Houthi movement did not immediately comment when contacted by Reuters.

Houthi officials in September visited Riyadh for the first time since the war broke out. That followed a first round of Omani-mediated consultations between Riyadh and Sanaa, running in parallel to U.N. peace efforts, when Saudi envoys visited Sanaa in April.

The peace initiatives gained momentum after archrivals Saudi Arabia and Iran agreed to reestablish ties in a deal brokered by China. A permanent cease-fire in Yemen would mark a milestone in stabilizing the Middle East.

"Grundberg expressed his deep appreciation for the key roles played by the Kingdom of Saudi Arabia and the Sultanate of Oman in supporting the parties to reach this point."

"He urged all parties to exercise maximum restraint at this critical time to allow for a conducive environment for dialogue and the successful conclusion of agreement on the roadmap."