The clash in the Qatif area comes as Saudi authorities try to root out suspected leaders of the protesters. Shiites claim they face discrimination and other abuses at the hands of the Sunni monarchy.
The official Saudi Press Agency reported on Thursday that the wanted man and a fellow gunman were killed during a gun battle. The report, citing an unnamed security official, says agents had traced them to a house on Wednesday.
More than a dozen people have been killed in clashes since late last year in Qatif, the kingdom's main oil export hub.