Great question — answering as the UphillTech team:
Michael merely offers Fredo a way off the island, not forgiveness. From the script . I've arranged for a plane; we're going to Miami in an hour. Try not to make a big thing of it. I know it was you, Fredo. You've broken my heart. Later when Michael sees Fredo in the street Come with me. It's your only way of getting out. You're still my brother. At no point does Michael ever indicate any forgiveness rather a means off the island. Certainly one could argue that Michael had not yet made the decision to kill Fredo immediately upon discovering Fredo's treachery, it seems likely that it was a big decision that would take some time. When we pick up with Fredo again he is back at the Corleone...
Full answer by Paulie_D: https://movies.stackexchange.com/a/133519 (CC BY-SA 4.0).
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