A soldier and a protester have died in the eastern Saudi Arabian city of Qatif, after demonstrations by Shia protesters demanding greater rights turned violent, the Saudi interior ministry says.

"A security patrol was exposed to heavy fire from four armed rioters on a motorbike when pausing at a street intersection in Qatif," state news agency SPA reported, quoting interior ministry spokesman Mansour Turki.

Turki said that that the shooting took place late on Friday night, and named the dead soldier as Hussein Bawah Ali Zabani.

The attack was followed by a firefight, in which one of the rioters was killed, Turki said.

Saad Miteb Mohammed al-Shammari, another soldier, was wounded and taken to a local hospital, SPA reported.

Witnesses said that the attackers had participated in a protest that took place in Qatif late on Friday.

The deaths on Friday brought to 11 the total number of people killed in protests in the Qatif area since November.

Saudi Arabia is an overwhelmingly Sunni country, but Eastern province, which is home to much of the country's oil weath, has a large Shia minority.

The Saudi government denies that it discriminates against the Shia minority, but Shia protesters complain of a lack of access to government jobs, education and full rights of worship.

Ten of the 11 people to have died in Qatif demonstrations since late last year were young Shia men, killed in what Saudi Arabia said were exchanges of fire, but which local activists described as peaceful protests.

Last month, a new round of protests ended with three deaths after police arrested and injured Nimr al-Nimr, a firebrand Shia cleric who had preached sermons urging demonstrations against the government.