The rebels launched the attack on the coast road from the government-held ports of Khokha and Mokha along which Saudi backed troops advanced on Hodeida earlier this week, the military source said.
They struck some 80 kilometres (50 miles) south of Hodeida, in a diversion from the frontline fighting around the city's disused airport.
Dozens of combatants have been killed since the offensive began on Wednesday and the United Nations has voiced concern for the vital aid shipments that pass through the city's docks.
Yemen rebel leader defiant as dozens die in battle for key port
Hodeida has been controlled by the rebels since 2014, when they drove the government out of the capital Sanaa and much of the country, prompting President Abedrabbo Mansour Hadi to flee into exile.
Saudi Arabia has since led the United Arab Emirates and other allies in a military intervention against the rebels.
The capture of Hodeida would be the coalition's biggest victory of the war so far and on Thursday rebel leader Abdel Malek Al-Huthi called on his forces to keep up their resistance and turn the coastal region into a "swamp for the invaders".
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