Chinese President Xi Jinping welcomed Indian Prime Minister Narendra Modi to his ancestral home province Thursday, highlighting ancient ties as the Asian giants reportedly discussed a simmering border dispute.

Attempting to put their relationship on a more personal footing, Xi met his visitor in Xian, the capital of Shaanxi province, telling him it was "the first time I have treated a foreign leader in my hometown", China's official news agency Xinhua said.

Modi, who was beginning a three-day visit, said it was "an honour to 125 crore (1.25 billion) Indians whom I am representing as Prime Minister", according to India's PTI agency.

The choice of venue was seen as reciprocation after Modi hosted Xi in his home state of Gujarat last year.

But ties between the world's two most populous countries have long been strained over a Himalayan border dispute that saw the two nations fight a brief, bloody war in 1962.

"Boundary issues were discussed including peace and tranquillity on the border," Indian foreign secretary S. Jaishankar told reporters following the summit.

He said the two also discussed India's attempt to join China as a permanent member of the United Nations' elite Security Council, which Beijing has avoided directly endorsing.

Both are members of the BRICS grouping of major emerging economies, but are jockeying for influence in Asia.

Beijing has vowed to pour investment into India's arch-rival Pakistan, as it rolls out plans to boost infrastructure across Asia which seem to mostly bypass India.

Chinese contracts to build or manage Indian Ocean ports have raised concerns it is seeking to establish a "string of pearls" in the region.

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.

The Indian leader will later head to the capital Beijing and China's financial hub Shanghai, seeking to deliver on election promises to attract foreign investment for India's crumbling rail and other infrastructure.

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

- Terracotta Warriors -

Xian is a former capital of China in Imperial times, and earlier Thursday, Modi inspected the emblematic Terracotta Warriors, pictures on his official Twitter account showed.

"The Terracotta Army is a heritage of the world," images on the social media network showed his comments in the visitors' book as reading. "It is a testimony to China's civilisational achievements."

He also toured the Daxingshan Temple, where Indian scholars are said to have translated Buddhist sutras into Chinese following its construction during the Western Jin Dynasty (265-316 AD).

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.

But his overtures have met with a mixed response in China.

Earlier this week an op-ed in the Global Times, affiliated with Communist Party mouthpiece the People's Daily, accused him of "playing little tricks over border disputes and security issues".

Writer Hu Zhiyong added that few Indians were able to understand Sino-Indian relations, due to "the inferiority of its ordinary people".

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