International pressure has mounted on Yemen's warring parties to end the war that has killed more than 10,000 people and pushed the country to the verge of starvation.
The move from the Houthi group came after the Saudi-led coalition ordered a halt in its offensive against Yemen's main port city Hodeidah, which has become the focus of the war.
"After our contacts with the U.N. envoy and his request to stop drone and missile strikes ... We announce our initiative ... to halt missile and drone strikes on the countries of aggression," Mohammed Ali al-Houthi, the head of the Houthis' Supreme Revolutionary Committee, said in a statement.
U.N. special envoy Martin Griffiths is trying to salvage peace talks after a round in September collapsed when the Houthis did not show up. He hopes to convene talks before the end of the year in Sweden to agree on a framework for peace under a transitional government.
Yemen's parties have given "firm assurances" they are committed to attending peace talks to be convened shortly, Griffiths told the U.N. Security Council on Friday, and pledged to escort the Houthi delegation from Sanaa if needed.
The Iranian-aligned group which has been battling the Saudi-backed government for nearly four years added it was ready for a broader ceasefire if "the Saudi-led coalition wants peace."
"(The decision) came to support the U.N. envoy, to show good faith and support the peace efforts," the statement said.
Saudi Arabia and the UAE both have said they support U.N.-led peace talks.
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 Saudi Arabia suspended temporarily oil exports through a strategic Red Sea channel following attacks on crude tankers.
Key Western allies including the United States have been urgently calling 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 early last month.