Apple (Nasdaq: AAPL) Chief Executive Officer Tim Cook apologized for the company’s iPhone warranty and repair policies in China after criticism over customer service in its second-largest market.

Apple is changing its practices to offer full replacements of older iPhones experiencing problems, Cook said in a letter posted on the company’s Chinese website. Apple also vowed to improve training, customer service, and monitoring of stores authorized to sell its products in China.

“In the process of studying the issues, we recognize that some people may have viewed our lack of communication as arrogant, or as a sign that we didn’t care about or value their feedback,” Cook said. “We sincerely apologize to our customers for any concern or confusion we may have caused.

The letter underscores China’s importance to Apple. The country, which is Apple’s biggest market after the U.S., accounted for $22.5 billion in sales in the 2012 fiscal year, and the company sold more than 2 million iPhone 5s there when that model went on sale there in December.

‘‘We have tremendous respect for China,” Cook said. “Our customers here will always be central to our thoughts.”

Some consumers in China had complained that Apple repaired broken iPhones instead of replacing the devices. While Apple said 90 percent of customers had been satisfied by the fixes, the company also said it would replace those handsets with new ones and offer a one-year warranty.

‘Deep Commitment’

“We recognize that we have much to learn about operating and communicating in China, but we want to assure everyone that we bring the same deep commitment and passion to China as we do to any other part of the world,” Cook said.

Apple still lags competitors in the country, where the average consumer earns less than $600 a month. The company is in sixth place, according to market researcher IDC, trailing competitors such as Samsung Electronics Co. and Lenovo Group Ltd., which offer devices in a range of styles and prices. Apple’s iPhone isn’t being sold by the country’s largest wireless carrier, China Mobile Ltd.

“At a minimum, these attacks put a wrench into Apple’s ability to strike a deal with China Mobile to open opportunities further in China,” Glen Yeung, an analyst at Citigroup Global Markets Inc., wrote in a research report. He has a neutral rating on the shars with a $480 target price.

Lost Sales

If Apple’s market share fell by half in China, it could result in $13.1 billion in lost sales, Yeung said. That’s the magnitude of market share Hewlett-Packard Co. lost in personal- computer sales in China after a similar media campaign hit that company in 2010, he said.

The apology comes after the People’s Daily, the official newspaper of the Chinese Communist Party, criticized the iPhone maker for poor service, including a March 27 commentary that said “Destroy Apple’s ‘Incomparable’ Arrogance.’” China’s central government also said it planned increase scrutiny of contracts with electronics makers, according to the official Xinhua News Agency.

Cook’s letter to Chinese iPhone users marks his second public effort to make amends with customers. He also apologized for the company’s mapping software in September after it was faulted for misguided directions and inaccurate landmark locations.

Apple has apologized for policies related to the iPhone before. Following the first iPhone release in 2007, co-founder Steve Jobs offered users rebates and an apology because early customers complained about a price cut two months after it went on sale.

In 2010, Jobs apologized and gave out free cases to customers because of antenna defects for the iPhone 4. After Consumer Reports and other publications showed the device would lose its signal if held a certain way, Jobs called a rare press conference to explain the issue.