According to the United Nations, nearly 300,000 Rohingya Muslims have fled Myanmar's Rakhine state into Bangladesh since August 25 when a fresh wave of violence erupted when militants attacked police posts in Myanmar's northern Rakhine state.
The Rohingyas allege that the military and Rakhine Buddhists responded with a brutal campaign against them.
Myanmar rejects this, saying its military is fighting against Rohingya "terrorists".
Ruling Awami League general secretary and senior Bangladesh minister Obaidul Quader said, "The entire world is today worried with the Rohingya issue and India also expressed its concern...their (India's) concern and stance beside us is very crucial at this moment."
Mr Quader recalled the decisive support given by India during Bangladesh's 1971 liberation war and said, "We hope India will favour Bangladesh in this humanitarian crisis as well."
Prime Minister Narendra Modi, who concluded his three-day visit to Myanmar on Thursday, expressed solidarity with the government there against the "extremist violence" in the Rakhine state.
PM Modi also urged all stakeholders to find a solution that respects the country's unity.
India also refused to be a part of a declaration adopted at an international conference recently in Indonesia as it carried "inappropriate" reference to violence in Rakhine state.
Bangladesh is facing a big influx of Rohingya Muslims from Myanmar.