Apple's much-anticipated launch of its iPhone 5 late last week left many would-be customers wanting.

Reports surfaced Monday about a lack of supply of the new phone, especially among the tech giant's retail partners such as Best Buy Co. Inc. and Target Corp.

Some Best Buy stores received as few as 10 new phones, while others received many more, according to a Wall Street Journal report Monday. The consumer electronics giant, one of the biggest sellers of iPhones and iPads, has about 1,100 stores in the United States.

In an e-mail statement, Best Buy spokesman Jeff Haydock said, "We have communicated to our pre-order customers that we are working on getting their phones and that we will notify them when product is available. We expect to fulfill all orders within 28 days, which is consistent with all retailers that carry the iPhone 5." He declined further comment on the supply issue.

Discounter Target said in an e-mail statement Monday that there was high demand for the iPhone 5 over the weekend. Spokeswoman Kristy Welker said "Target was able to fulfill many iPhone 5 pre-orders with the inventory we received, however, not all pre-orders were fulfilled."

Cupertino, Calif.-based Apple said Monday that it sold more than 5 million of its new iPhone 5 models three days after its launch on Friday in nine countries, including the United States.

Still, the company said demand for the iPhone 5 exceeded the initial supply and, while the majority of pre-orders have been shipped to customers, many are scheduled to be sent out in October.

Noting that demand for the new phone has been "incredible," Apple CEO Tim Cook said, "we are working hard to get an iPhone 5 into the hands of every customer who wants one as quickly as possible. He said stores continue to receive iPhone 5 shipments "regularly" and customers can order the device online.

"We appreciate everyone's patience and are working hard to build enough iPhone 5s for everyone," Cook said in a statement.

Over the years, Apple has been generating a growing percentage of its sales from its own website and the 326 stores it operates around the world, as opposed to retailers such as Best Buy. In fiscal 2011, Apple said sales from its retail business jumped 44 percent to $4.3 billion as it opened 40 more stores.

Some analysts were expecting Apple to sell 8 million to 10 million iPhones in the launch. BMO Capital Market's Keith Bachman told Barron's that the sale of 5 million units was "a bit of a disappointment," but the product is off to a strong start, nonetheless.

The issue with the iPhone 5 appears to be supply -- and not demand, Bachman said. "Consistent with past launches, most of the iPhone sales are being fulfilled by Apple directly, including online, instead of retail partners," he wrote.

Piper Jaffray's Gene Munster said in a report that his 8 million sales estimate assumed "full weekend availability." This opening-weekend shortfall "is reminiscent of the iPhone's debut shortfall in 2007, as well as the iPad launch shortfall in 2010. We would expect Apple to reach supply/demand equilibrium by the end of the December quarter," he wrote in a note to investors.

The phone, which sells for $199 in the United States, is to be released in 22 more countries on Friday, and in more than 100 countries by the end of the year.

Meanwhile, a brawl broke out in a iPhone factory in China that reportedly involved more than 2,000 employees. The fight erupted in a dormitory near a Foxconn Technology Group factory in the northern city of Taiyuan. China's official news agency, Xinhua, said 5,000 officers were dispatched to the scene where order was quickly restored and several people arrested, according to the Associated Press.

One of China's biggest employers, Foxconn makes iPhones and iPads for Apple, as well as products for Microsoft Corp. and Hewlett-Packard Co.

The Associated Press contributed to this report. Janet Moore • 612-673-7752