Apple Inc. has sold its millionth iPhone less than three months after the device’s debut, allaying investor concerns that demand had slowed.

Last week, the company, which had set out to sell a million iPhones by the end of this month, cut the price of the handset, which doubles as an iPod music player, by a third, to $399.

It took almost two years for Apple to sell a million iPods, the chief executive, Steven P. Jobs, said in a statement yesterday.

“As far as dispelling the fears that the iPhone was off to a bad start, this should help that,” said Gene Munster, an analyst at Piper Jaffray in Minneapolis.