I think it would depend on the context. If it was formal, I would say "nice to meet you too". By the way, one way to avoid this potentially awkward situation is to respond to an introduction with "How do you do" which looks like a question, but is one of many standard responses to an introduction.
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AnonymousWhat would be the answer after nice to meet you?It's not a question, so it doesn't need an answer. Just say the same thing.
kbee888By the way, one way to avoid this potentially awkward situation is to respond to an introduction with "How do you do" which looks like a question, but is one of many standard responses to an introduction. I see this neutral statement often used in business introductions.'How do you do?' sounds rather formal/old-fashioned to me these days.