"We received this morning the bodies of 10 people" killed in the attack on the HQ, a medical source at Ibn Sina public hospital in Mukalla told AFP.
A military official confirmed that at least three of the soldiers taken hostage by the militants were among the 10 dead.
"Efforts are ongoing to find other possible victims under the rubble," said the official who requested anonymity.
He added that "most parts of the building's third storey have been destroyed".
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"The armed forces have successfully completed the assault on the headquarters of the 2nd military region at Mukalla and have thoroughly cleansed it of terrorist elements," a defence ministry source was quoted as saying by the official Saba news agency.
"All terrorists who were in the building were annihilated," the statement added, without announcing the fate of captured troops.
Gunmen from the Al-Qaeda-affiliated Ansar al-Sharia group seized the complex on Monday and took an unknown number of hostages after a suicide bomber rammed a car into the entrance.
A military source told AFP that the army had fired on the building with artillery, without giving a number of casualties.
Mukalla is the capital of the southeastern province of Hadramawt and is a major port city.
Al-Qaeda in the Arabian Peninsula (AQAP) has intensified its attacks in southern Yemen.
On September 20, suspected Al-Qaeda fighters killed more than 50 soldiers and police in coordinated dawn attacks in neighbouring Shabwa province.
The armed Islamist network has taken advantage of the weakening of the central government since 2011, as a result of a popular uprising that toppled the then-president Ali Abdullah Saleh after 33 years in power.