Twelve militants were also killed when the ambush in Shabwa province sparked a firefight, tribal sources said.
Ten soldiers were also wounded and 15 captured, medics and an officer said.
The ground offensive, which was launched just hours before the opening of a donors' conference in London, seeks to capitalise on Al-Qaeda losses in a blistering US-backed air offensive last week in which nearly 60 suspected militants were killed.
Commanders are seeking to expel the jihadists from a series of smaller towns and hill districts in Abyan and Shabwa provinces where they retained a presence after a 2012 offensive in which the army recaptured the major towns.
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Militants ambushed the army convoy near Al-Saeed, one of several towns in Shabwa province where troops backed by militiamen advanced overnight, an officer said.
The army sent "massive" reinforcements to the area, another officer said.
Hours later, militants in Abyan province ambushed a seven-vehicle convoy advancing towards Wadi Daiqa, where Al-Qaeda suspects were positioned, an officer there said.