It is not as though we come to the end of the prophecy’s second section (Zephaniah 2:4 – 3:8) saying, The day of the Lord is over; what now?
Zephaniah 3:9–20 continues the study of what will happen in the day of the Lord (Zephaniah 3:11, Zephaniah 3:16, Zephaniah 3:19–20); the prophet turns from speaking about the furiousness of the day of the Lord (e.g., as described in Zephaniah 1:2–17) to answering the question raised by the call of Zephaniah 3:8 to wait for the Lord in confident expectation. Because the Lord so wills, the day is double-sided—and hope has the last word.
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9 “For at that time I will change the speech of the peoples to a pure speech, that all of them may call upon the name of the LORD and serve him with one accord.