Saudi Arabia has blamed the Iran-allied Houthis for firing a ballistic missile towards Riyadh airport on November 4. Two days later, the Saudi-led coalition responded by closing access to Yemeni ports.
This "could be considered as an act of war," Saudi Crown Prince Mohammed bin Salman said.
In a televised speech, Abdel-Malek al-Houthi said his group's ballistic missiles were capable of reaching the United Arab Emirates' capital of Abu Dhabi and anywhere inside Saudi Arabia.
At least 30 people were killed in an air strike that hit a small hotel north of the Yemeni capital Sanaa on Wednesday, the armed Houthi movement said.
Al-Qaeda in the Arabian Peninsula (AQAP), seen by the United States as the global network's most dangerous franchise, has exploited Yemen's war to expand its presence in the country's south.
Kuwait on Wednesday denied a Reuters report that Iran was using the Gulf Arab state's waters to smuggle weapons and equipment to Houthi forces in Yemen.
The Saudi-led coalition fighting in Yemen prevented a UN flight carrying aid agency staff from travelling to the Houthi-controlled capital Sanaa on Tuesday because three international journalists were also aboard.
The United Nations urged authorities in Houthi-controlled Sanaa on Thursday to investigate a "grave attack" on the convoy of its envoy to Yemen during his visit to the capital.
Thousands of Yemenis packed a square in the capital Sanaa on Sunday on the second anniversary of a war that has claimed the lives of more than 10,000 people and pushed the impoverished country to the brink of famine.