Shin Jong-kyun, president of Samsung's mobile communications business, said the Galaxy S III will hit the 10-million milestone within two months of its launch.
"It has been tough to keep up with demand," Shin told reporters.
Samsung's failure to procure sufficient mobile components for its latest smartphone has stoked concerns that its second-quarter smartphone sales could be much lower than expected. Shin said the company expects to resolve the supply issues with mobile components sometime in the next week.
"Despite the tough economic situation in Europe and problems with supplying components for the Galaxy S III, the second-quarter earnings will be better than the first quarter," he said.
Shares of Samsung tumbled 4.2 percent on the Seoul bourse on Monday, closing at a four-month low. The benchmark Kospi index fell 1.2 percent.
Samsung began sales of the Galaxy S III in Europe on May 29 and released it in the U.S. last week. In its home market, the company started sales of the latest iteration of Galaxy earlier Monday.
Samsung's sales estimate for the S III reflects robust demand from mobile operators. Unlike Apple Inc., Samsung does not disclose sales figures to consumers.
The South Korean company said the S III will be released by around 300 mobile carriers in 147 countries by the end of July, aiming for an early start before rival Apple announces a new version of the iPhone in the third quarter.
The third version of the Galaxy S features a bigger screen -- measured 4.8-inch diagonally -- but is thinner and lighter than its predecessors and the iPhone 4S.
Samsung packed the high-end smartphone with a legion of new features including eye-recognition technology that keeps the screen from dimming. It also has voice command functions that let users schedule an alarm or adjust volume by speaking to their device.
Its near-field communication technology enables sharing of data heavy multimedia content among Galaxy S III users quickly. But activating the function -- called S Beam -- takes multiple steps.
Because Samsung customizes its flagship smartphone based on Google's Android operating system, some of Samsung's features overlap with those made by Google.
Separately, Samsung's mobile president said it is still investigating the explosion of a Galaxy S III in Ireland. He said the battery wasn't the cause.
Samsung overtook Nokia as the world's biggest mobile-phone maker in 2011 and competes with Apple for the top smartphone maker position. It aims to double its smartphone sales this year to nearly 200 million phones.