The report by the SABA news agency said the government attacks began after militants tried to storm a military camp in the southern province of Abyan, where Islamist fighters have seized control of several towns.
The militant takeovers are part of widening chaos in Yemen since protests broke out in February calling for the ouster of President Ali Abdullah Saleh, who is being treated in Saudi Arabia for wounds sustained in an attack on his palace last month.
The SABA report added that two government soldiers were killed and 20 others injured in the Abyan fighting.
Al-Qaida's followers in Yemen, known as al-Qaeda in the Arabian Peninsula, is considered one of the terror network's most active branches and has been linked to several attempts on US targets, including the plot to bomb a Detroit-bound airliner in December 2009 and parcel bombs intercepted in Dubai and Europe last year.
The militant group leading the attacks in the Abyan area, Ansar al-Sharia, posted last month the names of 12 military officers it vowed to kill for taking part in crackdowns against its fighters.
In Saudi Arabia, the country's foreign minister, Prince Saud al-Faisal, said the health of Yemen president's is "generally good." He gave no further details on Saleh's condition or plans.