Relations between the world's two most populous countries have been in deep freeze since a deadly Himalayan border clash that killed 20 Indian soldiers and at least four Chinese troops in 2020.

Tens of thousands of soldiers have since been massed along both sides of the border. They remain despite 19 rounds of talks between top military officials of both countries.

The leaders met on Thursday while attending the BRICS summit in South Africa in what China's foreign ministry characterized as a "candid and in-depth exchange of views".

"President Xi stressed that improving China-India relations serves the common interests of the two countries and peoples," a ministry spokesman said on Friday.

"The two sides should bear in mind the overall interests of their bilateral relations and handle properly the border issue so as to jointly safeguard peace."

India's foreign secretary said Modi had highlighted unresolved issues along the Line of Actual Control (LAC) that divides India's Himalayan region of Ladakh from Chinese territory, where the deadly 2020 clash took place.

"Modi underlined that [...] observing and respecting the LAC are essential for normalizing India-China relationship," Vinay Kwatra told reporters on Thursday.

India has been wary of its northern neighbor's growing military assertiveness and disputes over the two Asian giants' 3,500-kilometer shared frontier have been a perennial source of tension.

China also claims all of India's northeastern state of Arunachal Pradesh, considering it part of Tibet, and the Asian giants fought a full-scale border war there in 1962.

Both countries have regularly accused each other of trying to seize territory along their unofficial divide, known as the Line of Actual Control.

The clash in 2020 along the border dividing Tibet from India's state of Ladakh led to a sharp deterioration in relations.

Modi's government has pumped billions of dollars into connectivity projects on its side of the border to boost civilian presence and establish new paramilitary battalions.

It is also seeking to develop closer ties with Western countries including fellow Quad members the United States, Japan and Australia, which are themselves wooing it as an alternative to China.

Nineteen rounds of military talks between Beijing and New Delhi, including the latest earlier this month, have failed to make headway on the border disputes.

Xi and Modi have both been present at numerous multilateral diplomatic meetings since the 2020 clashes.

But Thursday marked the first face-to-face encounter between the two leaders since a brief interaction at the Group of 20 Summit in Bali last November.