"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.
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Xiaomi claims sales of more than 61 million smartphones last year, up 227% from 2013, with turnover more than doubling to $12 billion.
But critics say the firm has simply copied the look of Apple's iPhones, thriving because of weak intellectual property protection in China.
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.
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.
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.
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