DENVER/SHANGHAIDENVER/SHANGHAI (Reuters) - Two U.S. airlines on Tuesday cut routes between China and the United States, underscoring increasingly tough competition from state-backed Chinese rivals as they aggressively expand their fleets with cut-price tickets.

American Airlines (AAL.O), the largest U.S. carrier by passengers, said it would drop a route between Chicago and Shanghai, canceling the second direct flight from the U.S. city to China in four months. It had canceled a flight to Beijing in May, although it still operates daily flights to the capital from Los Angeles and Dallas-Fort Worth, Texas.

"The two China routes ... have been colossal loss makers for us," said Vasu Raja, vice president of network and schedule planning, adding that high fuel costs had also made the route unsustainable.

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Hawaiian Airlines [HAII.UL] said it would from October suspend its thrice-weekly nonstop service between Honolulu and Beijing, which it opened in 2014, citing slower-than-expected growth in demand.

Competition from Chinese airlines is expected to grow with the anticipated easing of China's near-decade-old "one route, one airline" policy, which would allow more local airlines to fly long-haul international routes.

"U.S. airlines are at a severe disadvantage," said Mike Boyd, president of aviation forecaster Boyd Group. "The majority of demand is China-generated, and that gives Chinese carriers the advantage."

Chinese passengers arriving at U.S. airports are expected to nearly triple to 12.8 million in 2024 from 4.3 million this year, and the profile is shifting from groups to independent travelers, according to Boyd Group.

United Airlines UAL.N President Scott Kirby said Shanghai and Beijing had rebounded for the airline after several years of weakness, although revenue per available seat mile (RASM) was below levels of two or three years ago.

"We've had several years of weakness as there was an awful lot of capacity growth out of Beijing and Shanghai," Kirby said on the sidelines of the International Aviation Forecast Summit in Denver.

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American and Hawaiian said the route cancellations were unrelated to demands placed by China's civil aviation regulator on foreign airlines to amend the way they referred to Hong Kong, Macau and Taiwan on their websites.

Chinese state media had earlier this month singled out the two companies and other U.S. airlines as being among the last firms to comply with China's demands.

"That issue of how Taiwan was displayed on our website had absolutely zero impact on this decision," Hawaiian's chief executive, Peter Ingram, said. "Our economic evaluation was well underway long before that issue arose."