Loyalist forces backed by a Saudi-led coalition launched an assault to seize the Khaled Ibn Al-Walid base from Shiite Huthi rebels and their allies who had controlled it for over two years, military sources said.
After seizing a mountain overlooking the camp in recent days, forces loyal to internationally recognised president Abedrabbo Mansour Hadi had advanced on the camp from two directions, they said.
The camp, one of the biggest in Yemen, is 30 kilometres (20 miles) from the government-held Red Sea town of Mokha which pro-government forces retook in February.
Nine rebels were killed and two others wounded in twin coalition air strikes targeting three vehicles bringing reinforcements to the camp, military and medical sources said.
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They added that a further 12 rebels and four soldiers were killed in fighting overnight.
Loyalist forces launched a major offensive on January 7 to retake Yemen's 450-kilometre (280-mile) coastline as far as Midi, close to the Saudi border.
The Huthis, supported by troops loyal to former president Ali Abdullah Saleh, control parts of northern and western Yemen and the capital Sanaa, which they overran in September 2014.
Around 7,400 people have died in air strikes and clashes since then, the UN says. Aid agencies have warned of an impending humanitarian crisis in the Arab world's poorest nation.