By Ben Blanchard

BEIJING (Reuters) - Chinese leaders will woo Myanmar's opposition leader and Nobel laureate Aung San Suu Kyi on her first visit to the country, a snub for the quasi-military government whose fighting with rebels along China's border has angered Beijing.

But the visit will also be awkward for China's ruling Communist Party which has invited Suu Kyi, as her fellow Nobel Peace Prize laureate Liu Xiaobo remains in jail and Chinese President Xi Jinping is overseeing a sweeping crackdown on dissent.

Activists are putting pressure on Suu Kyi to make some reference to Liu's detention during the visit, and if she does, it will be a huge embarrassment for Beijing.

Suu Kyi will meet Xi and Premier Li Keqiang on the June 10-14 trip, according to her National League for Democracy (NLD), although China has kept details under wraps and it is not known if she will make any public appearances.

Since taking power in March 2011, Myanmar's reformist government has sought to decrease the heavy dependence on China that grew when Myanmar was a pariah state under military rule.

Beijing has watched nervously as the United States lifted some sanctions and engaged with the semi-civilian government.

But China has been keen to reach out to Suu Kyi.

The NLD is expected to do well in a general election in November, the first free vote in the country for 25 years.

Suu Kyi is excluded from the presidency under a military-drafted constitution, but her power and influence will grow if the NLD performs as well as expected.

The China-Myanmar relationship has been strained this year as stray army shells from fighting between the Myanmar government and ethnic Chinese rebels killed at least five people in China's southwestern Yunnan province in March.

Lin Xixing, a Myanmar expert at Guangzhou's Jinan University, said China was fed up with the government ignoring their protests on the border violence.

"Perhaps Aung San Suu Kyi can bring her influence to bear on ending the conflict," Lin said, adding it was highly unusual for Xi to meet any kind of foreign opposition figure.

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"In any case, it will be good to have her here to get to know her and explain our policy towards Myanmar."

Chinese state media has praised Suu Kyi ahead of her arrival, saying that with Myanmar's democratization the old certainties about the reliability of Sino-Myanmar ties were no longer there.

"We believe that Aung San Suu Kyi will become a good friend of China's," the Global Times, an influential tabloid published by the Communist Party's official People's Daily, wrote in an editorial.

The official Xinhua news agency added in its own commentary that it was important Suu Kyi develop "a very thorough understanding of the special bond between the two countries".

Suu Kyi led the NLD to a sweeping victory in general elections in 1990, but the military government refused to recognize the results.

She became an international icon after winning the Nobel Peace Prize in 1991 and spent most of the next two decades under house arrest where she continued to resist Myanmar's military rulers. She was freed in 2010.

Phyo Zayar Thaw, one of the two MPs traveling with Suu Kyi, said that he did not know if issues of human rights would be raised.

Hu Jia, a Chinese prominent dissident and close friend of Liu Xiaobo, told Reuters that if Suu Kyi does not call for Liu's release, "it will bring some degree of regret".

"Ms. Aung San Suu Kyi is a Nobel Peace Prize Laureate and in Chinese prison, there sits another Nobel Peace Prize Laureate," he said. "This is an unavoidable topic for the Chinese Communist Party and is extremely embarrassing."

(Additional reporting by Sui-Lee Wee, and Timothy McLaughlin in YANGON; Editing by Raju Gopalakrishnan)