PALO ALTO, U.S. -- Apple clearly intends to maintain its position in the high-end segment with the release of the iPhone XS and XS Max, but with price cuts for older models and the addition of the iPhone XR, CEO Tim Cook signaled designs on a bigger share of Asia's growing market.

"We want to serve everyone," Cook said in an interview with Nikkei. "We understand that there is a wide range of what customers are looking for and a wide range of prices that people will pay."

On Wednesday, the company announced price cuts for older models, including the iPhone 7 and iPhone 8, with the cost of the former now starting at $449 -- more in line with the midrange models of Apple's competitors.

On the premium side of the lineup, Apple now offers the 5.8-inch iPhone XS and the 6.5-inch iPhone XS Max, starting at $999 and $1,099, respectively. The XS Max has the largest screen on an iPhone yet, and both feature an organic light-emitting diode display.

"We always thought ... that if you provide a lot of innovation and a lot of value, there is a segment of people who are willing to pay for it," Cook said. "For us, it's a large enough group of people that we can make a reasonable business out of it."

Apple has been struggling to increase its share of rapidly growing Asian markets, where cheaper models of local makers dominate.

During the April-June period, Huawei Technologies surpassed Apple and moved into second place in terms of global shipments. The Chinese manufacturer's models often provide premium features but carry lower price tags than the iPhone range.

Cook justified the higher prices of the newest iPhones by noting their enhanced capabilities.

"A lot of things you were buying are now so convenient in one [gadget] and it has taken those things so much further than they could have ever ventured as a stand-alone device," he said.

"The role of the iPhone has become much larger in people's lives" than when it was first released in 2007, he argued.

In addition to competition from Asian makers, Apple faces a looming crisis in the trade war between the U.S. and China.

U.S. President Donald Trump has said tariffs covering an additional $267 billion of Chinese imports would be "ready to go on short notice," on top of a round of $200 billion already on the way.

The most notable targets for escalation would be electronics, especially a range of Apple devices, which had previously been spared. Many Apple products are assembled in China or use components produced there.

Cook declined to clarify how the company planned to mitigate the issue, simply saying that he was "an optimist."