Saudi police say two people have been killed and another two wounded by a gunman inside a bank in the southern city of Jizan, near the kingdom's border with Yemen.

The state-run Saudi Press Agency, quoting an unnamed Saudi spokesman, reports that security forces arrested the male suspect after surrounding the bank on Tuesday and forcing him to surrender outside.

The statement did not reveal the nationality of the suspect or say if he was attempting to rob the bank.

State-linked news websites showed amateur video of the arrest, with the suspect removing his shirt before putting his hands behind his head. An earlier image showed the suspect walking into the bank with what appears to be a rifle.