The battle near the town of Zinjibar in the southern province of Abyan killed 36 government troops and 25 of the militants, he said.
A medical official confirmed the death toll.
Scores were wounded from both sides, they said.
The official said the fighting was taking place west of Abyan's provincial capital of Zinjibar. Militants seized control of the town in May, taking advantage of political turmoil linked to the uprising against then-president Ali Abdullah Saleh.
Saleh stepped down last month in a US-backed power transfer deal that Washington hoped would allow Yemen's new leaders to move against al Qaeda. But the fighting highlights the difficulties faced by his successor Abed Rabbo Mansour Hadi in combatting the militant movement and restoring state authority in the lawless south.
The military officials said the militants were able to seize armoured vehicles, artillery pieces, assault rifles and rockets from the stores of an army base they attacked. Some of the heavy weapons were later used against the troops, causing most of the casualties on Sunday.
A defence ministry statement confirmed the clashes had occurred, saying the fighting began when militants detonated "booby trapped vehicles" at an army base in the region of Koud near Zinjibar. The wording of the statement suggested that the base had been occupied by the militants before army forces regrouped and took it back.
It said there were casualties on both sides but gave no figures.
Hadi meanwhile said in televised comments that fighting al-Qaeda and restoring security in the impoverished Arab nation were among his top priorities. He spoke during a meeting with leaders of Yemen's political parties.
Saleh, during more than 30 years in power, tolerated radical Islamic groups as part of a delicate balancing act that kept at bay threats to his authority in the fractured nation.
There has been a surge in attacks blamed on al-Qaeda after Hadi's inauguration.
Sunday's fighting followed the dismissal last week by Hadi's government of the military commander of the southern region, to which Abyan belongs, along with other security officials from the province.
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