In a televised speech, Houthi leader Abdul Malik al-Houthi vowed that the death of Samad - a relative moderate who helped oversee political and administrative duties while the Houthi military wing pursued fighting -would not split its ranks.
Yemen's Houthi movement has fired ballistic missiles at what it called "economic and vital targets" in the southern Saudi province of Jizan, where Saudi authorities said a man was killed by debris from the projectiles.
A police building adjacent to the Houthi-controlled ministry was also struck.The Houthis confirmed an air raid on Sanaa but gave no details.
An air strike on Yemen's capital by a Saudi-led military coalition has killed dozens of Houthi rebels including two commanders, according to a Saudi TV station.
The strike came hours before the Houthis staged a public funeral in Sanaa for Saleh al-Samad, a senior leader, who was killed on April 19 in an aerial attack claimed by the Saudis and their allies, this time in Yemen's coastal province of Hodeida.
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Jizan's civil defence spokesman Colonel Yahya Abdullah al-Qahtani told Saudi-owned Al-Arabiya television that a Saudi Arabian citizen had been killed by falling shrapnel. As the chairman of Yemen's Supreme Political Council, he was the second most wanted figure by the Saudi-led coalition. With at least 1,600 schools damaged or destroyed in the attacks, more than four million Yemeni children have been unable to attend school.
Al Maliki accused Iran of standing behind the instability in Yemen through arming the Houthi rebels.
The coalition has suffered a series of setbacks in recent months, with Houthis reportedly launching ballistic missiles and drones into Saudi Arabia and attacking coalition warships.
Yemen now stands at the brink of starvation.
The Saudi-led coalition imposed a total blockade on Yemen's ports in November in retaliation for cross-border Huthi missile attacks on Saudi Arabia.
The blockade has since been partially lifted, but access to the impoverished country remains limited.