Samsung Electronics (Seoul: 005930), the No. 1 smartphone maker, predicted sales next month of the new Galaxy S III model will top 11 million, including 10 million outside South Korea.

We're getting far better feedback on the model overseas than what we expected with the Galaxy S I and II, said Shin Jong-kyun, head of Samsung Mobile, when the phone was formally introduced in Seoul on Monday.

Shin said preliminary sales couldn't meet supply but that Samsung's factories are catching up fast. The Korean giant introduced the phone in 28 countries in Europe last month, in the U.S. last week, with the rest of the world scheduled for rollout next month.

The Galaxy III S, based on the Android OS from Google (Nasdaq: GOOG), has won good reviews from the trade press as well as newspapers including the New York Times and Wall Street Journal, which influence upscale buyers.

Samsung captured the biggest share in the smartphone sector in the first quarter from Apple (Nasdaq: AAPL), the world's most valuable technology company, market researchers reported.

Analysts for IDC previously said Samsung's share of the market was 29.1 percent, compared with only 11.3 percent a year ago. Apple's share fell to 35.1 percent from 18.3 percent a year earlier.

Samsung's share, of course, was captured by the earlier model, the Galaxy S II, which succeeded the S I. The two earlier models sold more than 50 million units since 2010, Shin said.

Samsung shares fell 50,000 Korean won (US $2.98) to 1.13 million won in Seoul on Monday. Shares of Apple, in Cupertino, Calif., fell $11.33 to $570.77  in Monday U.S. trading.

Apple, with the latest iPhone 4S as well as discounted versions of the older iPhone 3 and 4, is expected to introduce a major upgrade later this year. As usual, the company hasn't released product specifications, shipping dates or even the name of the new product, which will be manufactured by its usual Taiwanese vendor, the Foxconn unit of Hon Hai Precision Industries (Taipei: 2317).

Meanwhile, analysts Monday lowered some earlier expectations for exploding smartphone sales this year due to the easing of the global economy.

Goldman Sachs (NYSE: GS) analyst Simona Jankowski trimmed her forecast of mobile phone sales for the year to 1.84 billion from 1.95 billion, still a 4 percent annual increase.

Smartphone sales will rise 38 percent to 649 million, down from her previous estimate of 668 million.

Jankowski also attributed part of the slowdown to problems with some of the major suppliers including Canada's Research in Motion (Nasdaq: RIMM), the BlackBerry developer, and Finland's Nokia Corp. (NYSE: NOK).