South Yemen clashes wound senior officials
Mohammed al-Shaddadi and ex-minister Hussein bin Arab, who are close to exiled President Abedrabbo Mansour Hadi, were leading loyalist forces in the city of Loder at the time, the officials said without elaborating.
Like Hadi, both men are from Abyan.
Loder is the only town in the southern province that has not yet been recaptured by loyalist forces, who took provincial capital Zinjibar from the Shiite rebels and their allies on Sunday as they pressed an advance from second city Aden.
A medical source in Aden told AFP that 16 loyalist militiamen were killed and dozens wounded in Abyan over the past 24 hours, most when mines planted by the rebels exploded.
Loyalists secured Aden in mid-July and Lahj provincial capital Huta on August 4 before advancing on Abyan, backed by a Saudi-led coalition waging an air war against the rebels since March.
But rebels still control the capital Sanaa, which they seized last year, as well as large swathes of Yemen including the remote north where their mountain stronghold of Saada is located.
Clashes were also reported by residents in third city Taez on Monday, as well as in the central province of Ibb.