'House of Israel' in the Bible

However, God finds fault with them [showing its inadequacy] when He says,“Behold, the days will come, says the Lord,When I will make and ratify a new covenantWith the house of Israel and with the house of Judah;

“For this is the covenant that I will make with the house of IsraelAfter those days, says the Lord:I will imprint My laws upon their minds [even upon their innermost thoughts and understanding],And engrave them upon their hearts [effecting their regeneration].And I will be their God,And they shall be My people.