Abraham was born in the city called Ur Kasdim (. Traditionally this is the town known today as Urfa. It lies north of Haran - the town where Abraham lived many years before continuing his journey to Canaan. The region in which Urfa lies is called Aram Naharaim. It is thought to be the place of origin of the Kasdim or Chaldeans whose name forms part of Ur Kasdim. According to Josephus they are descended from Arphaxad, an ancestor of Abraham, while others connect them with Abraham's nephew Kesed. Aram Naharaim contains several towns which appear to be named after people with the same names as members of Abraham's family - the city of Nahor (the name of both Abraham's grandfather and brother), mound of Turahi [Terah], isle of Ragu [Reu] and city of Phalgu [Peleg], city of Serugh [Serug], city of Arpachiya [Arphaxad]. (The place called Haran [Charan] is however not related to the name of Abraham's brother Haran [Haran] - although they are spelt the same in English they are different words in Hebrew.)
A town named Ur was mentioned in writings found at Ebla. Some think that it was a town in the vicinity of Ebla while others think that it might be Urfa. One of Abraham's ancestors was named Eber and a king with that name ruled at Ebla .
Archaeologists in the 1920's discovered the ruins of an ancient city in the region of Sumeria, bearing the name Ur . Secular scholars assume that this is Ur Kasdim, a claim that is often repeated as if it were an established fact. This city was under the control of the Kasdim during the neo-Babylonian period. The name Sumeria comes from the Akkadian Shum-er and the root Shum is thought to be the Akkadian equivalent of Shem, the name of the son of Noah from whom Abraham was descended.
Regardless of which one of these places is the real Ur Kasdim, all of them lie within Biblical Israel as defined in Genesis 15:18-21. Ebla lies well west of the Euphrates and the Sumerian Ur also lies west of the Euphrates. The Euphrates is the eastern border of Israel according to Genesis 15:18. Urfa lies between the headwaters of the Euphrates proper. According to Genesis 29:1 this region - Aram Naharaim - was part of the land of the Bnei Qedem i.e. Abraham's family living in the east, who are also called Qadmonim or Kadmonites. According to Genesis 15:19 their land is part of Israel. It is true that Abraham was not born in Canaan, but Canaan was only one small part of Biblical Israel. The modern State of Israel is also just a small part of the full land of Israel of Biblical times.
Tanach,.Masoretic Text,. Mechon Mamre. Jerusalem, 2002