The reports came as the UN refugee agency UNHCR warned of a new displacement of civilians in the area.
The security sources said the air strikes yesterday and today hit five towns controlled by the Huthis around 70 kilometres (45 miles) south of Hodeida.
Medical sources said 28 Huthis were killed and 17 others wounded in the strikes.
There has been no let-up in the air campaign against the rebels that a Saudi-led coalition has been waging since March 2015.
At the same time forces of the Saudi-backed Yemeni government have stepped up attacks on the rebels and last week retook the Red Sea town of Khokha from the Huthis.
The security sources said new clashes broke out today as government forces tried to push towards Hodeida.
UNHCR said it was "bracing for further displacement and a spike in humanitarian needs as hostilities intensify in frontline areas on Yemen's west coast".
Hodeida is the main conduit for UN-supervised deliveries of food and medicine but the rebel-held port is controlled by the Huthis and remains closed, forcing the UN to divert aid supplies to other areas.
"As the port of Hodeida remains closed an additional 43 containers with emergency, shelter and household aid, including plastic tarpaulins and blankets for more than 20,000 families, had to be diverted to Aden," it added.
More than 2,000 people have died of cholera in Yemen this year, adding to the 8,600 killed in the conflict between the Saudi-backed government and rebels since 2015.
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