"This is a crucial moment for Yemen", he said, warning that a flare-up of fighting on the ground could derail the peace effort.
Griffiths said this week's sudden halt in an offensive by Saudi-led forces to try to recapture the city of Hudaydah was an important condition for a resumption of dialogue.
Rahbi said he believes the Houthis are not serious about the consultations.
Griffiths' last effort to get the parties together in Geneva in September fell apart, when the Iranian-backed Houthi rebels skipped the talks with Saudi-supported Yemeni government officials.
The almost four-year-old conflict has killed more than 10,000 people and caused a humanitarian disaster that could potentially threaten millions of lives.
Outside Hodeidah, Saudi Arabian and UAE-led attacks have struck people displaced by violence, while Coalition attacks have impacted downtown areas of the city, including around al-Thawra hospital on November 11, prompting hundreds of patients and staff to flee in terror.
"We support a peaceful solution in Yemen and we support the efforts of the United Nations special envoy to Yemen", Jubeir told a press conference, in which he separately said the Khashoggi case should not be politicized.
Turkey alleges the Saudis were responsible for his death and the United States announced Thursday it was imposing punitive sanctions on 17 Saudi officials who it said were responsible for or complicit in the killing.
Beasley will brief the UN Security Council on Friday with UN aid chief Mark Lowcock and UN Yemen Envoy Martin Griffiths, who is trying to broker peace in the more than three-year conflict seen as a proxy war between Saudi Arabia and Iran. Thousands of Yemeni civilians have died.
Beasley estimated $200 million (€175 million) per month would be needed to stabilize the currency and fend off economic collapse.
He said that will require scaling up assistance to help 12 million Yemenis, which would require about $150 million to $160 million a month.
Aid groups say they were able to get some food into the east of Hodeidah during the pause.
"We've had enough. It is time to start rebuilding Yemen, and Yemen will need every person in it to be rebuilt".
Britain, which oversees the Yemen file in the Security Council, said it would present a draft resolution with this package of requests on Monday to the council for its consideration.
"If starvation takes hold in Yemen then the enormity of the humanitarian task to try and keep people alive is mind-boggling", the envoy said, speaking in Amman, where he is based, before he flew to the US.
US deputy ambassador Jonathan Cohen told the council: "This war must end soon, and it won't end on the battlefield".
However, it is too soon to be optimistic with the cessation of hostilities.
Lowcock noted that after an upsurge in fighting immediately after his October 23 briefing to the council, there has been "a welcome de-escalation" in the last two days.
"I'm not asking that we end our alliance", Paul said.