So here is what you now must do. "Repent therefore and turn to God so that your sins may be wiped out" (3:19). It is too true that you murdered the Messiah of God, but God gives to you a second chance. Luke here uses metanoia for repent rather than the more common in the Greek Bible epistrepho (turn back) for "repent." Luke much prefers the former word, most especially made clear by Jesus' prophecy in Luke 24:47 that his followers would proclaim "in his name a repentance for the forgiveness of sins." And so Peter now proclaims to the Jews exactly that.
And that second chance is all well and good, but the church's history unfortunately more often gave to the Jews among them the back of their hands rather than an open-handed offer of repentance. Indeed, among the darkest pages of human history is the raw anti-Judaism, bleeding over (quite literally) into anti-Semitism, that has resulted from passages like Acts 3. We Christians cannot deny or parse or pass over our role in relegating our Jewish brothers and sisters to a dangerous second-class status, especially in light of the fact that not until the 1960s did the Roman Catholic Church finally remove from its official doctrinal claims that the Jews were "Christ killers." Only at the very end of his pontificate did John Paul II become the first pope in history to enter (!) the synagogue of Rome.
When we Christian preachers take up texts like these, we do so in the light of horrors too numerous to recount, of Jewish pogroms, of anti-Jewish actions and slogans and assaults of all sorts, and finally of the annihilation of Jews in the death camps of Europe. All these and more came out of texts like this one from Acts.
So, what to do? We cannot preach like Peter preached, despite what the old hymn, "There is a balm in Gilead," would have us do. We can share Peter's announcement of a new power in the world, the power of the resurrected Lord. But we cannot make as the substance of our preaching that the Jews, however ignorantly, murdered the Lord of Glory. Like that old hymn, our charge is to join Jesus in "making the wounded whole," healing the brokenness of a broken world, binding up the wounds of the world, many of which have been brought about by the very communities that proclaim "release to the captives and recovery of sight to the blind." The Christian church for far too long has added to the burdens of the world rather than moved to alleviate them. Let us begin by stopping now and forever our calumny against the Jews wherever it arises, even and especially when the Bible is its source. Surely, the resurrected Lord expects nothing less than that.