Al-Malki said Saudi air defense forces on Friday shot down a missile launched by Yemeni rebels at the southern Saudi border city of Najran.
A spokesman for the coalition said its forces attacked the global airport in the capital, Sanaa, and a nearby air base operated by the rebels, known as Houthis.
UN Secretary-General Antonio Guterres on Friday appealed for an end to the war in Yemen and laid out steps the parties in the conflict must take to move forward, warning that continued fighting would result in the country's worst starvation in a decade.
Without resolution to ongoing conflict, Yemen could face world's "worst famine" for decades, Antonio Guterres says.
Geert Cappelaere, Middle East director for the U.N. Children's Fund (UNICEF), described "heart-breaking" scenes of emaciated children in hospitals in the main port city of Hodeidah and the capital Sanaa, both held by Houthi insurgents.
Yemen has turned into a "living hell" for all children with thousands dying every year from malnutrition and easily preventable diseases, a top United Nations official says as Saudi Arabia presses ahead with its bloodshed and atrocities in the course of its three-and-a-half-year-old war against the impoverished country. He also said airstrikes by the Arab coalition, backed by the US, "must cease in all populated areas in Yemen".
Saudi Arabia and the United Arab Emirates lead a regional coalition that is seeking to oust the Houthis and restore Yemen's internationally recognized government.More news: Ndidi's last-gasp goal saves Leicester in draw with West Ham
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Earlier this week, the coalition sent more than 10,000 new troops towards Hodeidah ahead of a new offensive aimed at securing "areas liberated" from the Houthis, according to Yemeni government officials.
The port is the entry point for more than 70% of imports into the impoverished country.
Yemen has been at war since March 2015, when Houthis occupied northern Yemen, forcing the government into exile.
According to the World Health Organisation, almost 10,000 people have been killed in the conflict since 2015.
The Saudi-led coalition of Sunni Muslim nations is also wary of the spreading influence in the region of Iran's Shiite theocracy, widely said to be backing the Houthis.
Other rights groups estimate the toll could be five times higher.