Yemenis cautiously welcomed the announcement on Monday.
"We pray that this will be the real beginning of peace in Yemen, we are all tired of this war," said Mona Ibrahim, a teacher in the capital Sanaa, which has been under Houthi control since September 2014.
"We just want to live like other humans," Mohammed al-Ahdal, a resident of Hodeidah said.
The Houthi defence ministry said it would respond to any hostilities from the coalition.
Houthi-run Al Masirah TV reported later on Monday that Houthi forces fired a ballistic missile on Saudi-backed forces in the desert of Midi, bordering Saudi Arabia.
The Houthis say their missile attacks on Saudi Arabia are in retaliation for air raids on Yemen by the Western-backed coalition, which entered Yemen's war in 2015 to try to restore the Saudi-backed government of President Abd-Rabbu Mansour Hadi.
The coalition has carried out thousands of air strikes in the impoverished country that have hit schools, markets and hospitals, killing hundreds of people - though it says it does not target civilians.
The Houthis last July unilaterally halted attacks in the Red Sea to support peace efforts, after Riyadh temporarily suspended oil exports through a strategic Red Sea channel following attacks on crude tankers.
Western allies including the United States have called for a ceasefire ahead of the renewed U.N. efforts.
Western countries have provided arms and intelligence to the Arab states in the alliance, but have shown increasing reservations about the conflict since the murder of U.S.-based Saudi dissident journalist Jamal Khashoggi at the Saudi consulate in Istanbul last month.
