Human Rights Watch (HRW) also called on the government to ditch a proposal to lower the legal marriage age for girls from 18 to 16, which it said undermined the prime minister's recent pledge to end child marriage.
Bangladesh has one of the world's highest rates of child marriage, with two thirds of girls ending up as child brides. Nearly 30 percent wed before their 15th birthday and many are much younger.
Although child marriage is illegal, the law is widely flouted, with officials often forging birth certificates to facilitate underage marriages for small bribes, HRW said in a report, "Marry Before Your House is Swept Away".
Densely populated Bangladesh suffers frequent flooding and other natural disasters. The rights group said floods, cyclones and river erosion exacerbate child marriage by pushing families into greater poverty.
Read:Child Marriage Act: Monitoring committees to be set up
"Child marriage is an epidemic in Bangladesh, and only worsens with natural disasters," said Heather Barr, an HRW researcher on women's rights.
"The government should act before another generation of girls is lost."
Officials from the ministry of women and child affairs did not immediately return phone calls seeking comment on Monday.
At a global summit on child marriage in London last year, Prime Minister Sheikh Hasina pledged to end the marriage of girls under 15 by 2021 and all child marriages by 2041.
But campaigners say moves to allow girls to marry at 16 raise doubts about her commitment. A revised version of the original proposal would keep 18 as the legal age, but allow exceptions with parental consent. As most marriages are arranged by parents, campaigners say this would still amount to lowering the age to 16.
At the summit, Hasina also pledged a national action plan on child marriage, but HRW said this had not happened.
UNDER WATER
The report, based on scores of interviews with child brides, says marriage robs girls of their education and opportunities and puts their lives in danger when they are forced to have children before their bodies are ready.
Child marriage also increases the risk of domestic and sexual abuse, including marital rape.
Rashida, who was married at 10 or 11, is quoted as saying: "He forcibly entered me and I would cry so much that everything would get wet from my tears. It was so difficult, so painful. The first time, the next day I couldn't even move."
Driving factors behind child marriage include poverty, lack of education and dowry payments, which tend to be lower for younger girls. Environmental disasters drive the practice.
"Whatever land my father had, and the house he had, went under the water ... and that's why my parents decided to get me married," said Sultana who was wed at 14.
Other families describe feeling under pressure to marry daughters off fast for fear of losing their homes through river erosion.
HRW said the government must do more to raise awareness of the dangers of child marriage, enforce the law and keep girls in school, seen as one of the best ways to prevent child marriage.
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