Rehana Begum, 43, a British national from Stepney, died in Sunamganj on Friday, the Foreign Office has confirmed.
On Friday morning a man who said he was a family member phoned the BBC to say she had been killed for her valuables.
But local police have since told a BBC journalist the murder investigation is focusing on her family and whether there was a rejected marriage proposal.
Nazrul Hossen, Police Super of Sunamganj district, said when the victim disagreed in principle with that proposal, she may have been attacked with knives and hit on the head.
Police said she "died on the spot due to excessive bleeding".
'Hacked to death'Nobody has been arrested, but Mr Hossen said police were trying to find the culprits as soon as possible and said a murder case had been filed.
Earlier in the day, a man claiming to be a family member said Mrs Begum had been on holiday in the country with her husband and 12-year-old son since 17 July.
The man, who was calling from the south Asian country, said: "She came to Bangladesh to visit her family.
"She has been hacked to death by four people for jewellery and money."
A Foreign & Commonwealth Office spokeswoman said: "We are aware of the death of a British national Rehana Begum in Sunamganj, Bangladesh on 2 August.
"We are providing consular assistance to her family at this difficult time."

bbc.com