The exclusive carrier for the device in the country, China Unicom, said Tuesday that it signed up 5,000 iPhone subscribers in the first four days it was available. While that’s certainly not a blockbuster opening weekend, the carrier says it’s pleased nonetheless.

“We are satisified 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 Reuters.

It’s a difficult comparison when you measure the first weekend sales in China against the 146,000 AT&T signed up in the U.S. during the original iPhone’s first weekend in June 2007. Besides having to sell the device without WiFi, China has to contend with something U.S. carriers largely do not: a vast market for iPhone knockoffs.

China’s gray-market phone shipments are expected to reach 145 million units this year, a 44 percent increase over the 101 million shipped in 2008, according to market research firm iSuppli. For perspective, the worldwide (legally licensed) cell phone market is 1.13 billion, so the 145 million is a sizable chunk of that, almost 13 percent. Still, Apple analysts are already calling the phone’s debut in China “a disappointment.” Piper Jaffray’s Gene Munster said he was expecting China to contribute 1 million to 2 million iPhone sales to the worldwide total of unit sales for next year. Based on the weak opening numbers, he is revising China’s contribution to 550,000 next year.