Iran-backed Houthis were now in control of the Assilan, Bayhan and Ain districts in Shabwa as well as the Abdiya and Harib districts in Marib, said local officials and residents.
Hundreds of Iran-backed rebels have been killed in the battle for Marib in recent days, says the Saudi-led coalition backing the Aden government.
More than 156 Houthi rebels were killed and eight military vehicles were destroyed in an operation in Abdiya, south of Marib, says the Saudi-led coalition fighting the militants in Yemen.
The intensified fighting for the northern city leaves at least 50 Houthi rebels and Yemeni pro-government troops dead. The continuing clashes have reportedly claimed around 400 lives in September.
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.
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