Prime Minister Narendra Modi and his Italian counterpart Paolo Gentiloni, who held wide-ranging talks, also emphasised on the need for effective implementation of existing international commitments on countering terrorism, including the UN Global Countering Terrorism Strategy, UNSC resolutions and targeted sanctions relating to terrorism.
"In this context, the leaders also called upon all UN member countries to designate terrorist entities in line with the relevant UNSC Resolutions," said a joint statement issued after the talks.
While responding to a query on the Azhar issue, Chinese foreign ministry has said that "as for listing application by the relevant country, there are disagreements".
China is expected to block the move to ban Azhar again when the 1267 Committee of the UNSC takes up the issue on Thursday, the day the current hold on the proposal, piloted by the US, the UK and France, is expiring.
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Modi and Gentiloni also condemned in the strongest possible terms the recent terror attacks in India, Europe and elsewhere and emphasised on the need for strengthening international partnership and concerted action by the international community in addressing the menace of terrorism.
We are both committed to fighting terrorism in all its forms, and to strengthen our cooperation in cyber security," he said.
They also called on all countries to work towards rooting out terrorist safe havens, their infrastructure and networks and halting cross-border movement of terrorists, the joint statement said, in a veiled reference to Pakistan.
The leaders agreed to strengthen cooperation to take decisive and concerted actions against the al-Qaeda, ISIS, their affiliates and all other UN-designated globally proscribed terrorists and terror entities, including those mentioned in the India-EU joint statement on cooperation in combating terrorism. The statement was issued after the India-EU Summit earlier this month.
The two leaders also affirmed that terrorism should not be associated with any particular religion, nationality, civilisation, creed or ethnic group.
"They also expressed concerns at the growing misuse of internet towards radicalisation of youth and agreed to strengthen cooperation in combating radicalisation and violent extremism," the statement said.
They also agreed to explore the establishment of a bilateral dialogue on cyber issues.
In particular, they reaffirmed that international law was applicable in cyberspace and that there was a need to continue and deepen deliberations on the applicability of international law to cyberspace and set norms of responsible behaviour of states.
The leaders welcomed the holding of the 5th Global Conference on Cyberspace in New Delhi on November 23-24, it added.