Yemen has been rocked by growing instability since the Shiite fighters, known as Huthis, seized control of the capital Sanaa in September.
The Huthis have expanded their presence throughout the strife-torn nation in the face of fierce resistance from Sunni tribes backed by Al-Qaeda's powerful Yemeni branch.
Heavy Huthi shelling of a northern district of the central town of Rada killed five women late yesterday and displaced thousands, witness Jaber al-Zuba told AFP by telephone.
The sources said 30 Huthis were also killed in fighting around Rada.
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AFP could not immediately obtain an independent toll, and the Huthis rarely provide casualty figures.
Tribesmen in Rada said they destroyed two tanks and three armoured vehicles used by Shiite militias, also accused the army of backing them with heavy weaponry.
"The Huthis are using the army's equipment in the battle," one tribal source told AFP.
The rise of the Huthis has challenged the authority of President Abdrabuh Mansur Hadi, an ally of the United States, and violence has continued despite UN-backed efforts to find a political solution.
Saleh is a member of the Zaidi sect, an offshoot of Shiite Islam to which the Huthis belong.
A new cabinet, including members considered close to the Huthis, was sworn in Sunday in a bid to resolve the political crisis, despite calls for a boycott from both Saleh and the Shiite militia.
But authorities have yet to tackle the fighters in Sanaa or to impose order in other parts of the country where they have also imposed themselves.