The meaning of Ashurites in the Bible
(From International Standard Bible Encyclopedia)

ash'-ur-its (ha-'ashuri): According to the Massoretic Text of II Samuel 2:9, a tribe included in the short-lived kingdom of Ish-bosheth, Saul's son. A slight textual correction gives "Asherites," that is, the tribe of Asher; with this the Targum of Jonathan agrees. The tribe of Asher lay where it would naturally fall to Ish-bosheth's kingdom. The reading "Geshurites" (Vulgate and Syriac) is excluded by the known independence Of Geshur at this time (II Samuel 3:3; II Samuel 13:37). For similar reasons we cannot think of Assyria (Hebrew Asshur) nor of the Arabic Asshurim of Genesis 25:3.

See more on the meaning of Ashurites in the Bible:
Ashurites {Easton's Bible Dictionary}

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