I will put My words in His mouth.
This also clearly proves that the Prophet will teach something different. These are words which He has not yet put into the mouth of Moses or commanded; but He promises that He will do so in the future. Therefore this has to be a word other than the Word of the Law, which He had already most amply and perfectly given and commanded by the mouth of Moses, with such power that through its effectiveness it would drive those already terrified into death and despair. It would be vain to promise that it would be given and commanded if He had already done so by the mouth of Moses. Since, therefore, the future Prophet is to teach differently from Moses, His Word must not be the Word of the Law, which kills and terrifies, but a Word that makes alive and consoles. So we see that the prophets are instructed by this passage when they foretell another, future covenant, Word, and priesthood. Thus Jeremiah (31:31–32): “Behold, the days are coming when I will make a new covenant, not like the covenant, etc.”; and Ps. 110:4: “Thou art a priest forever”; and Is. 2:3: “The Word of the Lord will go forth from Zion, etc.”
Luther’s works, vol. 9: Lectures on Deuteronomy 1525