"We can't really fulfill Apple's requests. Our shipments are insufficient... given the huge market demand," Foxconn chairman Terry Gou told reporters late Wednesday.
He added that the design of iPhone 5, of which five million were sold over its launch weekend in September, has made the production difficult but did not elaborate.
He declined to say whether Foxconn plans to outsource some of the iPhone orders to other makers.
The iPhone has been a huge driver of Apple's phenomenal profits, along with the iPad, both of which are made by Foxconn, as other products by other firms such as Nokia, Intel and Sony.
Peter Oppenheimer, Apple's Chief Financial Officer, said on October 25 that demand for the iPhone 5 continued to outstrip supply, but it was working hard to catch up.
A lack of supply of the phones has hurt Apple's shares in recent weeks owing to concerns it may not be able to meet demand in the near future, which would in turn hit earnings.
Last month Apple said net profit in the July-September quarter climbed to $8.2 billion thanks to a 58 percent jump in sales of its phones and a 26 percent rise in tablet sales.