Apple Inc on Monday unveiled a smaller, cheaper iPhone aimed at new buyers, especially in emerging markets and possibly China, the world's biggest buyer of smartphones, as the technology company looks to reverse a decline in worldwide sales of its most important product.

The new device, called the iPhone SE, has a 4-inch (10-cm) screen and starts at a price of $399. It represents Apple's second bid for the crowded mid-tier market after an unsuccessful foray three years ago.

That is well below the starting price tag of $649 for the current top iPhone model without a contract, which is beyond the reach of many. The new phone, with Apple's vaunted A9 chip, doubles the speed of Apple's previous attempt at an entry-level phone, the 5s, launched in 2013. It also runs Apple Pay and comes in the wildly popular rose gold color.

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Shares of Apple were down about half a percent at $105.41 in early afternoon trade.

The more compact phone design comes after its expanded the size of the screens in its high-end iPhone 6 and iPhone 6 Plus phones in 2014 to as large as 5.5 inches. That was broadly seen as an attempt to match rival Samsung Electronics with its large-screen Galaxy phones.

Before the launch at Apple's leafy Cupertino, California headquarters, Chief Executive Tim Cook defended the company's refusal to comply with a U.S. court order to unlock an iPhone belonging to one of the shooters in a December attack in San Bernardino, California.

Apple has a responsibility to protect customers' data and privacy, Cook said, adding that Apple "will not shrink from that responsibility." His statement was greeted by applause from the audience.

The tech company's dispute with the U.S. government has become a lightning rod for a broader debate on data privacy in the United States. The company is set to square off against the U.S. government at a court hearing on Tuesday, likely the first round in a long legal fight to avoid being forced to decrypt the iPhone.