BEIJING (Reuters) - China has appealed for U.S. support in fighting Islamist militants in the far western Chinese region of Xinjiang, saying they are also a threat to the United States.

Chinese officials say the East Turkestan Islamic Movement (ETIM) recruits Uighurs, a largely Muslim ethnic minority from Xinjiang, and trains them with extremists in Syria and Iraq, with the intent of returning to China to wage holy war.

Many foreign experts, however, have questioned whether ETIM exists as the coherent group China claims it is.

The threat of terror grows "more complicated and severe by the day", China's Foreign Ministry said late on Tuesday, following a meeting between Chinese Vice Foreign Minister Cheng Guoping and Tina Kaidanow, Ambassador-At-Large for the U.S. State Department's Bureau of Counterterrorism.

"China stressed the serious threat of ETIM and other East Turkestan terror organizations to China, the United States and the international community, and requested that the United States vigorously support and coordinate with China in combating the efforts of East Turkestan terrorism forces," the ministry said.

Both sides agreed to combat cyber terrorism and violent extremism and strengthen anti-terrorism intelligence, it added.

Hundreds, perhaps thousands, of Uighurs, have illegally crossed the Chinese border in recent years, traveling to Turkey via Southeast Asia.

Rights groups say such migrants are fleeing ethnic violence in Xinjiang and Chinese controls on their religion and culture, allegations Beijing denies.

Hundreds of people have died in unrest in Xinjiang in the last three years, blamed by Beijing on Islamist militants. But Chinese officials have offered little evidence that the violence is linked to ETIM, which Washington deemed a terror group after the Sept. 11, 2001, attacks.

Some officials in the U.S. government have privately questioned the extent of the organization's influence in Xinjiang, though experts note that U.S. rhetoric on the group may be swinging back in favor of Beijing.

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China has ramped up counter-terrorism efforts following deadly attacks in recent years, including a mass stabbing in March 2014 at a train station in the southwestern city of Kunming in which 31 people were killed.

The government is on heightened alert ahead of an international athletics event in Beijing this month and a parade also in Beijing next month to mark 70 years since the end of World War Two.

"The bottom line is anti-terrorism work must be implemented well to ensure terrorist plots are foiled before they can be carried out," Xinhua news agency quoted deputy public security minister Huang Ming as saying.

(Reporting by Michael Martina and Ben Blanchard; Editing by Nick Macfie)