Zuhair al-Said was killed on Friday when police opened fire to disperse protesters in the town of al-Awamiya, in the Qatif region, they added.
Police said they were monitoring an unauthorised gathering in al-Awamiya when they were fired at by masked men.
Activists earlier said another man had been shot dead by police at another protest in Qatif on Thursday night.
Police again said unidentified gunmen had opened fire on a patrol, and confirmed that one person was killed and three others wounded.
‘Attacked’
Friday’s march was reportedly organised to protest against the killings of demonstrators, who have been calling since March for reforms, an end to sectarian discrimination and the release of political prisoners.
Qatif, in Eastern Province, is home to a Shia majority that has complained of marginalisation at the hands of the Sunni ruling family, the Al Saud.
“While security men were following up on an illegal gathering in the town of al-Awamiya in Qatif on Friday they were attacked by gunfire,” said a police statement published by the state news agency, SPA.
“They dealt with the situation by firing back, which resulted with the death of one,” it added.
One activist told the AFP news agency that eight armoured vehicles had been deployed in al-Awamiya to disperse the protest.
A photograph posted online by a Saudi Shia news website purportedly showed Zuhair al-Said on the ground after being shot in the stomach.
Another protester was shot dead last month in al-Awamiya. Seven protesters have now been killed since November, activists say.
Protests erupted in Eastern Province in March when the popular uprising in neighbouring Bahrain, which has a Shia majority and a Sunni royal family, was crushed with the assistance of Saudi and other Gulf troops.
About 500 people have been arrested since March. Activists say 80 remain in custody, including author Nazir al-Majid and human rights activist Fadil al-Munasif.
Source: BBC
