As a simple introductory statement for discussion:
The 'church' is the continuation and fulfillment of the everlasting gospel and covenant of the creator.
Acts 3:25 Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed. Unto you first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities. I believe this is the covenant that Noah carried through the flood also.
Their are 2 Israels;
One is of the spiritually similar "SEED" as the individual Jacob re-named Israel. This 'seed' of Israel is the similar idea as the 'seed' of Abraham as referring to a spiritual Genos of similar kind. John 1:11-13; Jer 31 (seed of Israel remains forever); Isaiah 61 talks of the seed of God; Ez 13; talks of the sons/daughters of faith individually delivering themselves out of 'that city'. And perhaps most noticably; Hosea 11, the whole chapter. This chapter again, like Jeremiah 31 associates Ephraim as the latter child of Grace through faith to those of all nations with "Israel" my Son. This 'spiritual' Israel is the church of all ages, under the Living God of Grace, truth and Mercy throughout all generations forever and ever...
The other "Israel" is the Israel of the national covenant delivered as a pattern, anti-type and shadow of the covenant of mercy. This national Israel began when Moses delivered the covenant on the first of the 11th (of 13) months 40 yrs after crossing the red sea. Deut 27:9; says 'this day' thou are become the people of God...hithertofor they were not a people, but now they were the people of God... Deut 5:3 says that the national covenant is different from the covenant of Mercy that He had made with their Fathers..(Abe, Isaac, Jacob). Deut 28-32 talks of the time from the Babylonian captivity through their return from captivity (Deut 30:1-4) and their hearing and response to the covenant of mercy and change of heart... (mid Deut 30)and then the end and 'latter end' of the covenant and nation in Deut 32 as administered through the Romans. This national Israel also contained people of faith and the covenant of Mercy and those who obeyed his commands. I think these two entities are considered by Daniel in his prayer when he talks of those to whom God gives mercy everlasting and those of 'thy people' whom were taken by the hand and led out of Egypt.
National Israel then WAS a parenthesis within Spiritual Israel of the spiritual children of the Creator and redeemer, full of grace and mercy to all who call upon Him.