Three men sought in connection with the abduction of a judge last month are already on a wanted list for their suspected involvement in terrorist attacks in eastern Saudi Arabia, the interior ministry said.

The judge, Sheikh Mohammed al-Jirani, disappeared in December from outside his home in Qatif province, where many of the conservative Sunni kingdom's Shi'ite Muslim minority live.

No group has claimed responsibility for his abduction but local media have suggested it may be related to his work for the Saudi government.

An interior ministry spokesman said three of the men believed to have taken part in the abduction were also among nine people wanted in connection with past "terrorist acts" in Qatif province and the eastern city of Dammam, including attacks on citizens and security personnel.

He named the three as Maitham Ali Mohammed al-Qudaihi, Ali Bilal Saud al-Hamad and Mohammed Hussein Ali Al Ammar.

Speaking at a news conference in Riyadh, the ministry spokesman, Mansour al-Turki, warned the kidnappers not to harm Jirani.

Turki also said authorities were holding three other men suspected of carrying out surveillance work that preceded the kidnapping.

Qatif is home to about one million mostly Shi'ite Muslims and is located in the oil-producing Eastern Province.

Since 2011 it has been shaken by frequent protests, mostly peaceful, though Shi'ite militants angry at what they say is repression of their community have sometimes attacked security forces in Eastern Province.