Abdulghani Jamil and his nephew Nasr Jamil "died of wounds sustained during late yesterday clashes between the governor's aides and Huthi militiamen", the sources said.
Jamil was appointed by fugitive President Abedrabbo Mansour Hadi, who fled to Saudi Arabia after the rebels seized power in Sanaa and later advanced on his last refuge in the south, the port city of Aden.
The Huthis "demanded Jamil hand himself over" to them. His refusal prompted a firefight in which both he and his nephew were wounded, the relatives said.