I am Peruvian by birth and I am an American citizen .. I was never asked for a Visa .. I think that as Americans we do not need a visa.
You don't need a Visa to visit Perú, neither to enter to Panama, but you need to buy a round trip ticket. They will ask you for the ticket to leave Perú.
I think if you can as an American citizen. But I'm not sure. You'll have to call both consulates so you're safer.
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