The informal meeting with 10 parents was held at Government House and the babies were born within a week or two of Prince George who was born in July last year, local media reported.
The royal couple started their three-week tour of New Zealand and Australia on Monday.
The Duke and Duchess of Cambridge plan to spend the next few weeks enjoying a wine tasting at a local vineyard, meeting with "The Lord of the Rings" director Peter Jackson, going on a jet boat ride and visiting Christchurch, which was devastated by an earthquake in 2011.
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