Indian Prime Minister Narendra Modi on Wednesday left for China on an official visit focused on boosting trade ties between Asia's rival superpowers and setting aside their historic mistrust.

Modi's office tweeted a picture of him waving from an Air India plane, marking his departure for the three-day trip to China, his first as premier.

After arriving in the ancient city of Xian, Modi will head to Beijing and the financial hub of Shanghai, seeking to deliver on election promises for foreign investment in India's crumbling rail and other infrastructure.

Ahead of his trip, Modi said he firmly believed "this visit to China will strengthen the stability, development and prosperity of Asia".

"I am confident my visit will lay the foundation for further enhancing economic co-operation with China in a wide range of sectors," he wrote on Twitter last week.

China is India's biggest trading partner with two-way commerce totalling $71 billion in 2014. But India's trade deficit with China has soared from just $1 billion in 2001-02 to more than $38 billion last year, Indian figures show.

Ties between China and India have long been strained over a border dispute stemming from a brief, bloody war the two nations fought in 1962.

After China, Modi will head to Mongolia and South Korea.

Modi led his Hindu nationalist Bharatiya Janata Party to a crushing victory last May on a promise to revive India's flagging economic fortunes.