The Iran-allied insurgents escalated their efforts to seize Marib, the government's last stronghold in northern Yemen, in February, and the fighting has killed hundreds on both sides.
The Houthis have been attempting since February to capture oil-rich Marib to consolidate their control over the northern part of war-torn Yemen.
Sources with the internationally recognised government say that 16 soldiers from their ranks were killed, including six officers.
Information minister has written in a Twitter post that the Houthis fired two ballistic missiles and two armed drones and had hit a mosque, a commercial centre and a women's correctional facility as well as ambulances rushing to the scene.
Meanwhile, Yemen's Houthi rebels said they had attacked and hit a military air base in southern Saudi Arabia with a drone, but the Saudi-led coalition fighting the group said it had intercepted and destroyed an armed drone fired into the kingdom.
Two officials from pro-government forces say that the rebels were mounting a concerted push that had left 26 loyalist soldiers dead as well as 44 from Houthi ranks.
The loss of Marib would be a heavy blow for the Yemeni government, currently based in the southern city of Aden, and for its Saudi backers.
The raids in Yemen's rebel-held capital come after the coalition said it intercepted 10 drones launched by the rebels on Sunday, in a sharp escalation in cross-border attacks on the kingdom.
The fighting in Marib has left 32 dead among government forces and loyalist tribes, while 58 Houthi rebels have been killed in coalition air strikes, government military sources say.
UN humanitarian agency says the risk of large-scale famine in the Arab world’s poorest country “has never been more acute."
Saudi-led military coalition says Iran-allied Houthis launched a ballistic missile toward Riyadh and three booby-trapped drones toward the province of Jizan, with a number of other drones being monitored.
Pro-government forces repelled the Houthi advances and reported heavy fighting that lasted "more than eight hours" in the Ablah region south of Marib city, a military source said.
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