The clashes broke out in the southern city of Zinjibar late Sunday, leaving at least seven militants dead and another nine wounded, according to Yemeni officials.
The officials spoke on condition of anonymity because they were not authorised to brief the media.
The rival factions are led by local commander known as Abu Anas al-Sanani and another known as Ossan Baliedy, the brother of Jalal Baliedy, the leader who was killed along with three others in a drone strike on Thursday.
He was believed to be ideologically closer to the Islamic State group, which is locked in a bitter rivalry with al-Qaida and has a branch in Yemen.
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Al-Qaida in the Arabian Peninsula, as the group's Yemen branch is known, has attempted several attacks on the US homeland and has long been seen by US officials as the group's most lethal affiliate.
It has exploited the chaos of Yemen's civil war, which pits various forces loyal to the internationally recognized government against Shiite Houthi rebels allied with troops loyal to a former president.
A Saudi-led coalition has been striking the Houthis since March 2015 and has also sent in ground troops. Today, the coalition shot down a ballistic missile launched toward the kingdom from Yemen, according to a statement.