Ansar al-Sharia made the claim about the tanks Sunday. There was no immediate comment from the army.
Clashes between U.S.-backed Yemeni armed forces and Ansar al-Sharia and its backers have taken place during the past month.
In an online posting, a member of the group said Yemeni armed forces backed by U.S. assistance "could achieve nothing through their airstrikes. We fully control Zinjibar, Waqar and Ja'ar while the army sustained huge losses," Bikyamasr.com reported Sunday.
Gov. Wahed Rashed of the port city of Aden warned the Yemeni government that Aden could be a strike target. He said al-Qaida militants were trying to gain a foothold in southern Yemen through the city.
Security analysts have said seizing Aden would offer a chance for al-Qaida to take control of the Red Sea through an alliance with al-Shabaab, a Somalia-based al-Qaida operation.