The army said it uncovered a large cache of weapons in homes used by the militants, including rockets and anti-tank weapons.
Fighting has built up over several days in Loder. The army distributed pamphlets over the weekend, urging civilians to flee, and security forces said "most" of the civilian population had fled by Tuesday.
'Only gunmen left'
The military's claims could not be independently verified: The city is surrounded by troops, so obtaining accurate information about the fighting is difficult.
Witnesses said the fighting intensified after Sunday night, when an ultimatum for fighters to surrender expired.
South Yemen, and Abyan province in particular, is thought to have become a base for the al-Qaeda affiliate known as al-Qaeda in the Arabian Peninsula (AQAP).
Foreign fighters, particularly from Saudi Arabia and Pakistan, are allegedly fighting with AQAP in the area.
Authorities said Adel Saleh Hardaba, 27, who they described as AQAP's second-in-command in Loder, was among those killed in the fighting.
In addition to fighting al-Qaeda-linked groups, Yemen's government is battling a separatist movement in the south and a Shia rebellion in the north. That latter conflict may be related to the current siege, said Mohammed Al-Qadhi, a Sana'a-based journalist with The National newspaper.
"The government is trying to use al-Qaeda as a pretext to attack movement activists who are pushing for independence for the south," he said.