Nearly 500 are sheltered in a cleared-out chicken farm in a Hindu hamlet in Bangladesh's southeast, a couple of miles from where most of the 421,000 Rohingya Muslims who have also fled violence in Myanmar since August 25 are living in makeshift camps.
The Hindu refugees say they are scared of going back to their villages in Buddhist-majority Myanmar's restive Rakhine state, but also wary of staying in mostly Muslim Bangladesh.
Prime Minister Narendra Modi's government has made it easier for Hindus, Buddhists, Christians and other minorities from Bangladesh and Pakistan to gain citizenship in India.
"We just want a peaceful life in India, not much. We may not get that in Myanmar or here," he said. Fellow refugees nodded in agreement, stating that they wanted the message to reach the Indian government through the media.
The Indian government declined to comment on the Hindu refugees' hopes. A government source said it was waiting while the Supreme Court hears an appeal against the home ministry's plans to deport around 40,000 Rohingya Muslims from the country.
But Achintya Biswas, a senior member of the Vishwa Hindu Parishad (VHP), or the World Hindu Council, which has close ties with the Rashtriya Swayamsevak Sangh, the ideological parent of the ruling BJP, said India was the natural destination for the Hindus fleeing Myanmar.
"Hindu families must be allowed to enter India by the government," Mr Biswas said by phone. "Where else will they go? This is their place of origin."
India's Home Ministry spokesman KS Dhatwalia declined to comment.
A senior home ministry official in New Delhi, speaking on condition of anonymity, said that no Hindu in Myanmar or Bangladesh affected by the violence had approached Indian authorities.
"At this juncture we have no SOS calls from Hindus," said the official. "Also, the Supreme Court is yet to decide whether India should deport Rohingya Muslims or not. The matter is sub-judice and any policy decision will be taken only after the court's order."
"WANT TO FEEL SAFE"
Hindus make up a small but long-standing minority in both Myanmar and Bangladesh.
Refugee Rudra, a barber from Myanmar's Thit Tone Nar Gwa Son village, showed Reuters what he said was a temporary citizenship card issued in 1978 by the authorities there. The card listed his race as "Indian" and religion as "Hindu".
Since then, rights monitors and fleeing Rohingya say the army and Rakhine Buddhist vigilantes have mounted a campaign of arson aimed at driving out the Muslim population, leaving many villages in northern Rakhine empty.
"Our village in Myanmar was surrounded by hundreds of men in black masks on the morning of Aug. 25," said Veena Sheel, a mother-of-two whose husband works in Malaysia.
"They called some men out and asked them to fight the security forces ... a few hours after we heard gunshots."
Ms Sheel left the next day with eight other women and their families, walking for two days to reach Bangladesh.
"There are so many people all around us. No peace here, no peace back in Myanmar," said Ms Sheel. "We should be taken to Hindustan, that's our land. Wherever we stay, we want to feel safe."
It also plans to nearly halve to six years the period Hindus, Christians and other minorities from those countries need to have lived in India to be granted citizenship by naturalisation.
"We are regularising only those who have come due to religious persecution in Bangladesh and Pakistan," junior home minister Kiren Rijiju told Reuters last month, adding that there was no policy on refugees from Myanmar.
It will not be easy for secular India to accept the Myanmar Hindu refugees' demand while the government is pushing for the deportation of Rohingya Muslims.
The Indian government has already been criticised by activists for not speaking out against Myanmar's military offensive, and accused of vilifying the Rohingya in the country to seek legal clearance for their deportation.