But Beijing gave no assurance on supporting New Delhi's bid on a UN ban against Pakistan-based militant leader Masood Azhar,
"Both sides recognised terrorism as a key issue. President Xi said we should strengthen our security dialogue and partnership," External Affairs Ministry Spokesperson Vikas Swarup told reporters.
Modi and Xi Jinping met at a beach resort here, ahead of the BRICS Summit to review bilateral ties and its dimensions.
Swarup said that Xi underlined that "terrorism and violent extremism were on the increase", alluding to the threat from the Islamic State terror group.
"The Chinese side is very well aware of our concerns, and the need for us to ensure that globally notified terrorists are designated by the UN," he said, adding that the two sides are coordinating on the issue and talks would continue over it.
The Spokesperson said that the Modi and Xi also had a "brief discussion on" India's prospects of joining the Nuclear Suppliers Group (NSG).
"PM Modi said we look forward to working with China to realise India's membership of the NSG," he said.
Swarup said that one round of dialogue has already been held on this issue and the second would be conducted soon.
This apart, both leaders expressed satisfaction at the increase in high-level visits between the two countries.
Modi and Xi agreed that bilateral investment and economic cooperation has increased.
Xi said that Chinese companies were being encouraged to invest in India, according to Swarup.
Modi also appreciated China's contributions to the BRICS and said the New Development Bank of BRICS nations was a symbol of partnership of the member states of the grouping.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)