Apple's Chinese partner sold 5,000 iPhones in the country after the handset made its debut last week, but is still hopeful it will increase the number of its third-generation mobile users by more than 1 million a month.

China Unicom said it's signed up more than 5,000 iPhone users in China since the phone went on sale on Friday and it expects the Apple phone to boost its average revenue per user.

Meanwhile, in the US and Europe, iPhone 3GS sales reached 1 million within three days of its June debut.

We are satisfied with iPhone sales so far, and we aim to have an additional 1 million new 3G subscribers each month in the near future, China Unicom Chairman Chang Xiaobing told Bloomberg.

Apple, based in Cupertino, California, had expected to sell about 500,000 iPhones initially in China via Unicom, according to a research note by Barclays’ analyst Ben Reitzes.

Demand will increase to several million over the next few years, Reitzes noted.

He expects overall sales for the iPhone in the December quarter of 7.5 million units.

China is a higher consumer of mobile technology, with 719.8 million mobile-phone users at the end of September, after adding 9.3 million in the month, according to government data.

The price tag for a 32GB iPhone 3GS in mainland China: 6,999 yuan, or $1,024, which doesn't include the service contract. Meanwhile, in Hong Kong, a 32GB iPhone 3GS costs $800.

Even though the iPhone only recently made its official debut in China, there are a lot of unofficial iPhones out there. iPhonAsia's Dan Butterfield estimates there's some 1.5 million grey-market iPhone owners in China, with more than a third of those iPhones running on China Mobile's Edge 2G network.

Apple stock today is down $1.28, or 0.6 percent, to $188.09.