The official said yesterday, the army succeeded in regaining control over one district on the outskirts of Zinjibar, but the rest of the provincial capital was still in al-Qaida's hands.
The official spoke on condition of anonymity because he was not authorised to speak to reporters.
A Defense Ministry statement yesterday said the offensive that started two weeks ago around another city in the southern Abyan province, Lawder, has so far killed 250 al-Qaida militants.
Also, 37 Yemeni soldiers have died, it said.
During a year of internal turmoil that eventually led to longtime Yemeni President Ali Abdullah Saleh's resignation, al-Qaida took advantage of a security vacuum to overrun parts of the south.
The US believes al-Qaida's branch in Yemen is the most dangerous arm of the terror group because of its repeated attempts to carry out attacks in the US.
In recent weeks, the Yemeni military has been hitting the militants in ground and air operations, while al-Qaida has carried out some bloody surprise attacks of its own against government forces.
Yemen's government expressed determination.
"The war on terrorism will expand and reach all the terrorist elements; it will continue and will not stop until it curbs it and uproots it," a statement yesterday from the Ministry of Interior read.
Under a power transfer deal brokered by Arab Gulf countries and backed by the United States, Saleh received immunity from prosecution in return for stepping down.
Protesters have been on the streets ever since, rejecting the terms.
The new president, Abed Rabbo Mansour Hadi, has pledged to purge Saleh's loyalists and family members from top security and military posts, a step toward restructuring the army to enable it to effectively combat al-Qaida militants in the south.
Hadi's decisions have met with stiff resistance from the Saleh's allies.