"In the next five to 10 years, Xiaomi has the opportunity to become the world's number one smartphone company," Lei Jun told the Chinese-organised World Internet Conference.
Xiaomi, which takes its name from the Chinese word for millet, has excelled in China's cut-throat smartphone market by delivering high-performance products at cheap prices.
In less than five years, the Chinese company has become the world's number three smartphone vendor, behind only Apple and South Korea's Samsung, shipping 17.3 million phones in the third quarter of 2014, according to International Data Corp (IDC).
Xiaomi claims sales of more than 61 million smartphones last year, up 227 percent from 2013, with turnover more than doubling to $12 billion (roughly Rs. 75,713 crores).
But critics say the firm has simply copied the look of Apple's iPhones, thriving because of weak intellectual property protection in China.
Apple has never taken legal action against Xiaomi, but in a veiled reference to the firm, the US giant's senior vice president of design Jony Ive has called similarities between their products "theft", the Wall Street Journal reported.
(Also see: Xiaomi Hits Back at Apple's 'Theft' Accusation)
A spokesman for Xiaomi's marketing department told AFP: "We hope these biased people can put down their tinted glasses, examine Xiaomi's practices and experience our products and then make a fair appraisal."
'Millet and rifles'
Beijing-based Xiaomi has come from nowhere, growing from a 2010 start-up in Zhongguancun China's "Silicon Valley" to a company valued at $45 billion (roughly Rs. 2,83,924 crores) after its latest funding round in December, when the founder of e-commerce giant Alibaba Jack Ma was among the investors.
Like Apple founder Steve Jobs, Lei, 45, has a fondness for black tops and jeans, and he told a panel at the Internet conference in Wuzhen in November: "In this magic land, we produced not only a company like Alibaba, but a small miracle like Xiaomi."
A serial entrepreneur and angel investor, he has a string of successful companies and investments, including software developer Kingsoft and online retailer Joyo.com which was bought by Amazon.
Explaining why he chose the name Xiaomi, Lei has said: "We want to conquer the world using millet and rifles," using a phrase coined by Chinese leader Mao Zedong.
The second character "mi" can also stand for mobile Internet or "mission impossible" in English, he added.
One analyst called Lei "the last but most important ingredient for the success of Xiaomi".
In China, Xiaomi ranks second with a 13.5 percent share of the domestic smartphone market, according to consultancy Analysys International. Samsung is first with 15.4 percent and Apple lags at 6.9 percent as of the second quarter last year, the latest available figures.
Xiaomi initially left alone the "high-end mobile phone market dominated by Apple and Samsung" said Zhang Yi, chief executive officer of China-based iiMedia Research, and took on "the vast middle- and low-end markets not satisfied by other domestic phone makers".
It created a user-friendly interface based on Google's Android operating system, he said, "seized the growing trend for mobile Internet in China and topped its peers with high-performance but low-priced products".
Xiaomi's devoted users are indifferent about accusations of imitation.
"I don't mind whether it is really copying Apple. Xiaomi's user experience is pretty good and I won't buy an Apple because of high prices," user He Ling said.
Xiaomi's high-end Mi 4 lists for $410 (roughly Rs. 25,800) with 64GB of memory, less than half the $998 (roughly Rs. 62,800) Chinese retail price of a comparable Apple iPhone 6 (Review | Pictures). Its newly-launched Redmi 2 budget model is only $115 (roughly Rs. 7,200).
For its part Apple's products are popular in China, but it has faced problems in the massive market, only linking up with the country's biggest mobile phone service provider in late 2013.
Last year's iPhone 6 launch in China was nearly a month later than other major markets as Beijing delayed regulatory approval and called for improvements in security of personal data.
(Also see: iPhone 6 Given Approval for Sale in China)
But while Xiaomi is a major player in China, analysts say that patent issues and low brand recognition outside its home market are obstacles to the international expansion necessary to realise Lei's dream.
"What remains to be seen is how quickly the company can move beyond its home territories to drive volumes higher," market intelligence provider IDC said.
Xiaomi has launched products outside mainland China in Hong Kong and Taiwan, as well as Southeast Asia, but the company suffered a setback in India.
In December, Sweden's Ericsson won a court order blocking sale of Xiaomi devices in India over patents, Bloomberg News reported.
Wang Jun of Analysys International told AFP: "Even if Xiaomi were able to sort out all of its intellectual property problems in overseas markets, it would still take years for it to overtake Apple's market position."