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The retailer had already made the same warning to PlayStation 5 pre-order customers last week.
“We are making every effort with the supplier to procure more inventory,” the message to customers reads. “We will provide additional updates once more information becomes available.”
It’s not clear if this issue is only affecting North American customers or also Amazon’s international sites.
Microsoft has said it plans to make more Xbox Series X and S consoles available on launch day after “record-breaking” demand for the next-gen systems.
Xbox Series X and S pre-orders opened earlier this week, with the premium console in particular quickly selling out, according to reports.
Xbox rival Sony made more PlayStation 5 stock available to retailers this week following its own sell out pre-order operation last week.
Daniel Ahmad, senior analyst at Niko Partners, told VGC he expects supply issues for both PlayStation 5 and Xbox Series X this year.
“While production is ramping up and component scarcity is less of an issue than before, we believe that logistics issues will be a barrier for both platform holders to overcome this holiday, with the impact from Covid-19 leading to long shipping times and shortages on store shelves during the launch period.
“We expect Sony and Microsoft to utilise air shipments, which will cost more, to meet demand this year.”