Along with its land border dispute with India and sea boundary disputes with several other neighbouring countries in the South China Sea, China also has tensions with Mongolia.
The recent election of China critic Khaltmaa Battulga as Mongolia's new president has strategic implications and PM Narendra Modi has already reached out inviting him to India.

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Strategic counterbalance against China in Asia is part of PM Modi's “Act East“ policy. Faced with growing Chinese pressure, Mongols look to India as a new power to countervail Beijing. Stronger ties with India provide Ulan Bator with options that it would otherwise not have in its dealings with Beijing.
Following the 2016 blockade of Mongolia by China, Beijing took note of India's $1 billion credit line to Mongolia.Significantly, Beijing termed it as a bribe while Mongolia's request for help from India was described as politically hare brained by the Chinese official media.Though neither side wants to provoke, India-Mongolia cooperation nonetheless signals to Beijing that as China expands its footprint in South Asia, India can play the geopolitical game in China's backyard.

For historical reasons, Mongols fear and loath the Chinese more than the Russians. Therefore, irrespective of what Nepal or Bhutan may or may not do, Mongols will continue to hedge their bets.
Should Battulga follow through on his anti-China campaign rhetoric, Beijing will use all means at its disposal, blandishments and bluster to ensure Mongolia does not go too far.
