Japan's second-largest mobile carrier KDDI will sell Apple's new iPhone, the California-based company said, ending rival operator Softbank's highly profitable reign as the sole provider in Japan.

Shares of Softbank fell 2.3 percent in morning trade, while KDDI fell 0.5 percent and market leader NTT Docomo slid 1.4 percent. That compared with a 0.8 percent fall in the benchmark Nikkei average.

The market response may have been muted by the fact that the reception for the iPhone 4S, unveiled on Tuesday in California, was lukewarm compared with the rapturous welcome sparked by previous models.

Softbank will put the iPhone 4S on sale on October 14, while KDDI said it has not yet decided when it will begin to offer the latest version of the hugely popular smartphone.

Having KDDI sell the iPhone may liven up the whole smartphone market, said analyst Shinji Moriyuki of SMBC Nikko Securities in Tokyo. I think more people will switch from feature phones.

The move, reported earlier by Japanese media, comes after Apple opted for similar strategies in other markets, with Sprint becoming the third operator to offer the iPhone in the United States, after AT&T and Verizon.

Analysts say the loss of de facto exclusivity will be a blow for Softbank, Japan's third-largest mobile carrier, which saw profits balloon after it threw its weight behind the iPhone even as other carriers expressed skepticism that it would take off in a market dominated by feature phones from domestic makers.

Softbank has long been criticized by users for its patchy network quality, and risks losing iPhone fans to its rival.

To lose that effective exclusivity does give them a little bit more head wind. They will have to work harder, said Nathan Ramler, an analyst for Macquarie Capital Securities.

It may be only a matter of time before Docomo, with half of Japan's 120 million mobile phone users, also takes a bite of Apple's newest offering, possibly spurring an increase in total iPhone sales in Japan.

The trend everywhere is for the iPhone to be offered by multiple cell service providers, which would suggest that Apple may extend itself further, said Macquarie's Ramler.

I expect over time to see a similar trend in Japan, he said.

(Reporting by Poornima Gupta in California, Isabel Reynolds, Tim Kelly and Maki Shiraki in Tokyo; Editing by Michael Watson and Chris Gallagher)

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