This is what Moses spoke to Israel at Sinai in the Septuagint (Greek translation of the Old Testament). Ἰδοὺ τὸ αἷμα τῆς διαθήκης, ἧς διέθετο κύριος πρὸς ὑμᾶς περὶ πάντων τῶν λόγων τούτων. (“Behold, the blood of the covenant, which the LORD has decreed with you concerning all these words.” Note: “the blood of the covenant… the LORD…”)
This is what Jesus speaks to the disciples during the Last Supper (Mark 14:24): τοῦτό ἐστιν τὸ αἷμά μου τῆς διαθήκης τὸ ἐκχυννόμενον ὑπὲρ πολλῶν. (“This is my blood of the covenant that is poured out for many.”)
Several things are taking place here. (1) Moses offers the blood of an animal at the inauguration of the Mosaic Covenant, which is between Israel and God, while Jesus offers his own blood between himself (!) and his Jewish followers. (2) Given the parallel wording of the accounts, it would be negligent to see the literary agreement as occurring fortuitously. Mark intends to communicate that Jesus was in fact establishing a covenant by means of his own blood. (3) Jesus covenants directly with his followers. While the divine identity is strongly implied for any first century Jewish reader, in our own present day the truth is drowned out by historical critics who scoff at the idea that Jesus “of Nazareth” had a self-understanding that included divinity. It remains that Jesus’ audience would have understood that Jesus was functioning in the place of God who makes covenants. There is an implicit claim to deity in Jesus’ covenant-making. (4) By identifying himself with God, Jesus, who gives his own blood, becomes God who dies for the forgiveness of sins. (Though this part comes from Matthew’s Gospel.) (5) The new covenant of Jesus is marked, then, by the forgiveness of sins.
This is first-century Jewish thinking. Not simply the stuff of fourth-century Gentile councils.