Apple sold more than a million iPhone 3G cellphones its first weekend — with some stores running out — and two million more since then, analysts say. But its July debut has been nothing less than a public relations headache for AT&T, with eager buyers complaining about dropped calls and poor network connections.

Some fingers point to Apple, which has tried to deflect the complaints. But many others point to AT&T’s cellular network. Whatever the source of the problems, AT&T’s rivals, long irritated by all the attention the iPhone has received, are on the attack and happy to exploit the discontent.

“A phone is only as good as the network it’s on,” said a full-page Verizon Wireless newspaper ad on Thursday, lobbing a shot at AT&T’s 3G, or third generation, high-speed network. A Verizon executive sent an e-mail to Wall Street analysts last week: “So much for a ‘new’ way of doing business at the old AT&T — your father’s phone company.”

For AT&T, the nation’s No. 1 wireless carrier, which exclusively offers the iPhone, the situation is especially tricky because the stakes are so high. Apple’s customers are largely forgiving of any foibles of the iPhone’s maker. But wireless companies like AT&T and Verizon are afforded no such a luxury. The 3G network is supposed to make it easier to surf the Web and watch videos online. With nearly 90 percent of all Americans owning a mobile phone, there is little room to grow and these rivals can ill afford to lose customers.

Further aggravating consumers, neither company has fully explained why calls were dropped and the network was slow. Theories abound, which is causing even more confusion — and finger-pointing. Is it a problem with the phone itself? Richard Windsor of Nomura Securities surmised in a research report that a new radio chip made by Infineon, a German chip maker, was to blame for the iPhone’s spotty service in areas where the cellular signal was weak.

Since Americans are not the only iPhone users complaining — consumers in the Netherlands reported iPhone problems too — some analysts think the iPhone is partly to blame. Apple offered a software fix to mixed reviews — but no explanation. Most analysts put the onus on AT&T. “If consumers are not getting the full 3G experience, that is not Apple’s fault,” said Akshay K. Sharma, a research director of carrier network infrastructure at the Gartner Group, a consulting firm.

Nielsen Mobile, a consulting firm, said that in tests in the 47 largest American cities, it was able to connect to 3G networks 93 percent of the time. (Its sample included all carriers.) By contrast, in the San Francisco area, where many of the iPhone troubles have been reported, that number was 87 percent.

Phil Marshall, of the research firm the Yankee Group, said the problem probably lies somewhere in between, in how the iPhone interacts with AT&T’s network and signals are transmitted and received.

AT&T’s growing pains with its 3G network might otherwise be overlooked if not for the popularity of the iPhone. (Verizon executives conceded they too had problems when data users increased use of their highest speed network.) AT&T’s 3G network includes 310 cities with 100,000 people or more, but it plans to add 40 cities by the end of the year.

“It’s hard to launch an iconic device like the iPhone on a network that it is not yet fully deployed,” said Mr. Marshall. “As they build these networks they will need to make more improvements or the complaints will persist.”

But there is a bigger issue at play too, Mr. Marshall said. “Both companies are accustomed to controlling all aspects of the delivery of its products,” he said. “It illustrates the culture clash, when you create an environment where you share the responsibilities between them. Then you have problems.”

Already there seem to be fissures in the relationship. Two camps are emerging at AT&T: those who think Apple is too controlling with information and those who think Apple can do no wrong, said two people who have talked to AT&T executives but who declined to be named because they were not authorized to speak on their behalf.