Parliament passed the Child Marriage Restraint Act last night, replacing a law dating back to the British colonial period.
The new rule keeps the minimum marriageable age for males at 21 and for females at 18 but relaxes the restriction for "special circumstances" - including for girls who elope, are raped or bear children out of wedlock.
Rights groups have criticised the law, saying it would jeopardise the gains Bangladesh has made in cutting the levels of child marriage and improving the health of women and children.
The coalition, which includes international charities such as Save the Children, Action Aid, national charities and rights groups, said the law could be abused and poses a "risk" to children.
But a ruling party lawmaker who heads parliament's committee on women's and child affairs said it reflects the reality in villages where 70 per cent of Bangladesh's 160 million people live.
She said the special circumstances in the law are aimed at protecting rights and giving dignity to children born out of wedlock.
Despite making impressive gains in many social indicators in recent decades, child marriage remains rampant in the conservative Muslim-majority country.
Bangladesh currently has one of the world's highest rates of child marriage.
According to figures posted by UNICEF on its website, 66 per cent of girls are married before the age of 18 and over a third before the age of 15.
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