Leonard, this is a complicated subject that I have only recently come to understand better, as it isn't really taught correctly most of the time. Israel is still the same people that God has made covenant with today as was in the Old Testament. In the New Testament, we see this:
Acts 13:23 Of this mans seed hath God according to his promise raised unto Israel a Saviour, Jesus:
You will find that people's knowledge of who Israel is varies greatly from church to church and people to people.
All of Israel is both houses of Israel and then all the people who have decided to come within the covenant given to them by God through Abraham, the father of our faith. This promise is in the Old Testament and in the New Testament:
Hebrews 8:6 But now hath he obtained a more excellent ministry, by how
much also he is the mediator of a better covenant, which was
established upon better promises. 7 For if that first covenant had
been faultless, then should no place have been sought for the second.
8 For finding fault with them, he saith,
Behold, the days come, saith
the Lord, when I will make a new covenant with the house of Israel and
with the house of Judah:
10 For this is the covenant that I will make with the house of Israel
after those days, saith the Lord; I will put my laws into their mind,
and write them in their hearts: and I will be to them a God, and they
shall be to me a people:
Jer 31:31 "
Behold, the days are coming, says the LORD, when I will
make a new covenant with the house of Israel and with the house of
Judah-- 32 not according to the covenant that I made with their
fathers in the day that I took them by the hand to lead them out of
the land of Egypt, My covenant which they broke, though I was a
husband to them, says the LORD. 33 But this is the covenant that I
will make with the house of Israel after those days, says the LORD: I
will put My law in their minds, and write it on their hearts; and I
will be their God, and they shall be My people.
Ro 4:16 Therefore it is of faith, that it might be by grace; to the
end the promise might be sure to all the seed; not to that only which
is of the law, but to that also which is of the faith of Abraham; who
is the father of us all,
If your interesting in knowing more, there is a portion of a book available to read online that explains many things at this link:
http://www.aarons-advocates.org/BACONT.html