He said India had already voiced its concerns over the gravity of the crisis and held "very high level conversations" with Bangladesh and Myanmar.
"The fact that there is an exodus of a large number of people from the Rakhine state in Bangladesh is clearly a matter of concern. Our objective will be to see how they can go back to their place of origin. That is not easy," he said.
The foreign secretary was responding to a question on the crisis at an event organised by the Carnegie India in New Delhi.
"We feel that this situation is better addressed through practical measures and constructive conversation rather than doing very strong condemnation. We need a lot more sober, realistic (and) locally sensitive approach," Mr Jaishankar said.
In a communication to all states, the Union home ministry had said the rise of terrorism in last few decades has become a serious concern for most nations as illegal migrants are prone to getting recruited by terrorist organisations. It has also directed the state governments to set up a task force at district levels to identify and deport illegally-staying foreign nationals.
In September, in response to a petition, the Centre had told the Supreme Court that the Rohingya refugees were a serious security threat as many of them have links with terror organisations and Pakistan's Inter-Services Intelligence (ISI).
On October 13, the apex court had said the Rohingya refugee problem was of a "great magnitude" and the state would have to play a "big role" in striking a balance between national interests and human rights while dealing with this case.