The adviser, General Mohsen Saeed al-Ghazali, was killed along with the soldiers in Azzan, a city in Shabwa province which the army retook from militants on Thursday last week, a military official said.
Today's attack comes five days after the defence minister, Mohamed Nasser Ahmad, escaped unscathed along with two senior security officers when gunmen ambushed their convoy as they returned from the south.
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An army officer on the ground told AFP that troops on Wednesday "repelled two simultaneous attacks by Al-Qaeda" on army positions in Azzan and Jul al-Rida, killing three attackers and wounding others.
The attacks sparked clashes between troops and jihadists in which eight soldiers were also wounded, the officer said.
Residents in the area said several cars and homes were damaged in the exchange of fire, and that many families in Azzan have been fleeing the city due to the violence.
The authorities in Sanaa have put security forces in the capital on alert for revenge attacks following the army's recapture of Azzan, with the United States also closing its embassy.
The interior ministry said this week that checkpoints were set up around the provinces of Sanaa, Ibb, Baida, Lahij and Marib to prevent the entry of jihadists fleeing the offensive focused on Shabwa and Abyan -- both in the south.
Yemen's air force killed five Al-Qaeda suspects in a raid yesterday on a convoy carrying weapons and ammunition.
On Monday, a drone strike killed six Al-Qaeda suspects in Marib.
AQAP took advantage of a 2011 uprising that forced veteran president Ali Abdullah Saleh from power to seize large swathes of southern and eastern Yemen.
The army recaptured several major towns in 2012 but has struggled to reassert control in rural areas, despite the backing of militiamen recruited among local tribes.
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