"It's not easy to make the iPhones. We are falling short of meeting the huge demand," Foxconn Chairman Terry Gou told reporters after a business forum.
However, he declined to comment on brokerage reports saying that the group's other unit, Foxconn International Holdings (FIH), had taken on some production.
Hon Hai Precision Industry, the main listed entity of the parent Foxconn Technology Group, is the key assembler of Apple's iPhones.
The group also owns FIH, which traditionally assembles non-Apple products, such as phones from Nokia Oyj and Huawei Technologies Co Ltd.
Shares of Foxconn International Holdings Ltd (FIH), the world's biggest contract maker of cellphones, surged as much as 35 percent on Monday after Citigroup upgraded the stock to a 'buy' and said it expected the firm to start assembling iPhones this year.
Shares of FIH fell 5.7 percent in Hong Kong on Wednesday, while Hon Hai was up 0.6 percent in Taipei. (Reporting by Clare Jim and Lee Chyen yee; Editing by Anne Marie Roantree)
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