After the talks between Prime Minister Narendra Modi and Tusk, the two sides underscored the need for early return of the displaced people of all communities to northern Rakhine state in Myanmar.
Addressing a joint press event, Tusk said the two sides wanted de-escalation of tensions and full adherence to international obligations in Myanmar and access of people to humanitarian aid.
"The Rohingya people must be able to return voluntarily with safety and dignity. We call for implementation of recommendations of the (Kofi Annan-led) International Rakhine Advisory Commission to tackle the root cause of this crisis. As a neighbour India stands first in the line to respond," Tusk said.
Millions of Rohingya Muslims have fled the conflict-hit Rakhine state to Bangladesh and India after the escalation of tensions following a military crackdown.
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The joint statement said both sides took note that the violence was triggered by a series of attacks by Arakan Rohingya Salvation Army (ARSA) militants which led to loss of lives amongst the security forces as well as the civilian population.
"India and the EU expressed deep concern at the recent spate of violence in the Rakhine state of Myanmar that has resulted in the outflow of a large number of people from the state, many of whom have sought shelter in neighbouring Bangladesh," the joint statement said.
The joint statement said India and the EU also recognised the role being played by Bangladesh in extending humanitarian assistance to the people in need.