Around 15 of the dead were killed in fighting north of the militant stronghold of Jaar, a town in Abyan province that has been controlled by the militants since last year.
The al Qaeda-linked Ansar al-Sharia (Partisans of Islamic Law) exploited last year`s popular protests against former president Ali Abdullah Saleh to capture swathes of territory in Abyan, including the provincial capital Zinjibar.
The expansion of the militants` area of control has unsettled the United States and Saudi Arabia, both targets of failed attacks by Yemen`s al Qaeda wing (AQAP), which this week claimed responsibility for a suicide bombing in the capital Sanaa that killed more than 100 soldiers.
This month the government began a counter-offensive against Ansar al-Sharia with U.S. help.
A military official said the army had managed to recapture key positions in Zinjibar, where at least 63 militants were killed on Saturday in heavy fighting, many of them Somalis.
The bodies of seven militants were seen on Sunday being carried away from a factory located west of Jaar, which is used by Ansar al-Sharia as a base, after it was attacked by a Yemeni warplane on Saturday night.
The United States and Saudi Arabia have been pushing Yemeni President Abd-Rabbu Hadi Mansour, who took over after Saleh stepped down in February, to unite the army and roll back the militants` gains.
Washington considers Al Qaeda in the Arabian Peninsula (AQAP), the group`s Yemeni wing which has attracted fighters from Somalia and Saudi Arabia, as its most active cell.
American intelligence and counter-terrorism officials say their ability to conduct operations against AQAP inside Yemen, notably with drone strikes, has improved significantly since Hadi took office. (*)