The belief in New Delhi is that Rohingya refugees will increase India's terrorism exposure, which is already at high levels amid threats from Pakistan-based insurgents.
The Rakhine crisis has triggered warnings of extremist violence around the region as organisations like Al-Qaeda urge followers to avenge the Rohingya. New Delhi is particularly concerned that Rohingya refugees could be members of the Arakan Rohingya Salvation Army, or ARSA.
Officials believe ARSA, an armed militia responsible for August's attack on Burmese security forces, may be linked to trans-national fundamentalist networks, but the Rakhine-based group has rejected such claims.
Modi is also worried about the impact on ally Bangladesh, according to Sajjanhar.
Dhaka's capacity to accommodate refugees "is bursting at the seams," with Prime Minister Sheikh Hasina under increasing pressure from opposition parties close to Pakistan ahead of 2018 general elections, Sajjanhar said.
Hasina has requested Yangon to take back the refugees, but Myanmar's de-facto leader Aung San Suu Kyi said on Tuesday that her country would only open its doors to "verified refugees." Her country refuses to grant the Rohingya citizenship.
"India should show leadership by protecting the beleaguered community and calling on the Burmese government to end the repression and atrocities causing these people to leave," said Meenakshi Ganguly, South Asia director at Human Rights Watch, noting that New Delhi had a long record of helping vulnerable populations from neighboring countries, including Sri Lankans, Afghans and Tibetans.