In Sanaa, the rebels said they had discussed the establishment of a government, and said they would respond "positively" to any attempt to end the conflict.
Meeting in Riyadh, the Yemeni cabinet gave an "initial welcoming to the ideas that came out of the meeting in Jeddah," which included US Secretary of State John Kerry, the government's sabanew.net website said late Saturday.
Kerry announced a fresh international peace initiative to resolve the 17-month-old conflict after meeting Thursday with Gulf counterparts, a British minister and the UN envoy to Yemen.
The plan offers Huthi rebels and their allies participation in a unity government but demands their withdrawal from Sanaa and other key areas, as well as surrendering heavy weapons to a third party.
The rebels had been demanding a unity government as the first step towards resolving Yemen's war.
On Sunday, they said they had "discussed the necessary steps for the establishment of a government in the shortest possible time", at a meeting of the recently created "Supreme Council" in the capital.
The rebel-controlled news agency said they also gave the assurance that they would "respond positively to any initiative on stopping the aggression and lifting the blockade... and on achieving the desired peace".
Signup to our newsletter and follow us on Facebook and Twitter!
The internationally backed government of President Abedrabbo Mansour Hadi wanted a rebel pullout from seized territory, including Sanaa, and a surrender of weapons, as the first steps, in line with a UN Security Council resolution on the crisis.
On Saturday, the government stressed its "readiness to positively deal with any peaceful solutions".
But it said any proposal should comply with UN Resolution 2216, sabanew.net reported.
A foreign ministry official said Yemen has not officially received the new initiative, adding that UN envoy Ismail Ould Cheikh Ahmed was tasked with delivering it to the warring parties.
UN-sponsored talks in Kuwait collapsed in early August after three months.
Kerry said on Thursday that Yemen's war "needs to end as quickly as possible".
A Saudi-led coalition launched a military campaign in March 2015 against the rebels in support of Hadi who had holed up in his refuge in Aden before being forced into exile.
More than 6,600 people, mostly civilians, have been killed since March 2015 and more than 80 percent of the population has been left in need of humanitarian aid, according to the UN.