The UAE has trained and armed thousands of Yemeni fighters, mostly in southern provinces and western coastal areas, as part of the forces battling the Houthis, who control most urban areas including the capital Sanaa and the main port of Hodeidah.
The conflict in Yemen began with the 2014 takeover of Sanaa by the Iranian-backed Houthis, who toppled the government of Abed Rabbo Mansour Hadi. A Saudi-led coalition allied with Yemen's internationally recognized government has been fighting the Houthis since 2015.
The draft resolution, seen by Reuters, authorizes UN Secretary-General Antonio Guterres to deploy - for an initial 30 days - an advance team to begin monitoring and to support and facilitate the deal between the warring parties.
As outrage over the murder of Saudi dissident Jamal Khashoggi in Istanbul by Saudi operatives fused with concern about Yemen, a wave of disquiet swept Washington amid accusations that the US military could be complicit in war crimes.
The US official's reassurances of continued support comes as Sweden hosts the first UN-led peace talks in two years between the warring parties and as Gulf Arab leaders hold an annual summit in Riyadh on Sunday, expected to discuss the war.
Mohammed Ali al-Houthi said the Iran-backed rebels ordered the cessation of rocket and drone attacks on the Saudis and forces loyal to coalition member the United Arab Emirates at the request of U.N. special envoy Martin Griffiths.
The Houthis last July unilaterally halted attacks in the Red Sea to support peace efforts, after Saudi Arabia suspended temporarily oil exports through a strategic Red Sea channel following attacks on crude tankers.
The move, announced by the coalition on Saturday and confirmed by Washington, comes at a time when Riyadh, already under scrutiny for civilian deaths in Yemen air strikes, is facing global furore and potential sanctions over the murder of journalist Jamal Khashoggi .
The US has provided the Saudis and their UAE coalition partners with intelligence, aerial refueling and military advice, but U.S. forces are not directly involved in the airstrikes or other aspects of the fighting.
Many Yemenis who have fled their homes and farms in and around Hodeidah to head north to the Houthi-held capital Sanaa or to safer areas along the western coast and the southern port city of Aden said that they are struggling to survive.