More than 436,000 refugees have crossed the border from Myanmar's Rakhine state since August 25 when a military crackdown was launched following attacks on security forces allegedly by Rohingya militants.
"We are fully supportive of Bangladesh," India's High Commissioner to Bangladesh Harsh Vardhan Shringla said.
"We will continue to stand beside Bangladesh diplomatically and humanitarian way," he said during an event to mark the signing of a cooperation deal between a Bangladeshi and an Indian health facility in the presence of Bangladesh's Foreign Minister AH Mahmood Ali.
External Affairs Minister Sushma Swaraj earlier expressed India's full support to Bangladesh's stance over Rohingya issue as international alarm is growing over the fate of the Rohingyas who continue to flee Rakhine State in Myanmar.
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The Indian envoy's comment came ahead of a meeting of Bangladesh's foreign ministry with envoys of the Security Council member states here to explain its suggestions to resolve the crisis.
Bangladesh has put across its proposals to resolve the Rohingya crisis as the UN Security Council met on the issue, Ali said.
The 15-member UN Security Council met behind closed doors yesterday to step up its response to the exodus of 480,000 Rohingya Muslims after a military crackdown in Rakhine State.
The UN earlier condemned as "ethnic cleansing" and international community called "genocide" echoing Bangladesh's concerns.
Ali said Dhaka "does not want to go into a conflicting situation" as it expected smooth repatriation of "forcibly displaced Myanmar nationals", who fled their home on the face a military offensive.
Envoys of the US, the UK, France, Russia, China, Sweden, Italy, Egypt and Japan were present in the meeting held at the State Guest House Padma here.
Ali said the envoys were called in to the diplomatic briefing as part of Dhaka's efforts to "sensitise further" the crucial UN organ about the humanitarian crisis.
He said that Bangladesh would also speak as the Security Council was set to hold an open debate on the issue at the UN headquarters in New York tomorrow.
UN Secretary-General Antonio Guterres will publicly brief the Security Council tomorrow on the crisis as seven of the 15 member states have requested the meeting.
Ali said that the Union Minister for Office of the State Councillor U Kyaw Tint Swe was expected to arrive in Dhaka next month although the exact date was yet to be finalised.
Diplomats said the Security Council could consider adopting a formal statement if the situation does not improve.