The "Cycle of Fear" report has been jointly prepared by the Geneva-based World Organization Against Torture (OMCT) and local rights group Odhikar.
The government, however, dismissed the allegations as "baseless", Efe news reported.
The report is based on detailed examinations of more than 300 cases of torture spanning the period 2009-2017 investigated by Odhikar as well as on information gathered from victims and other relevant groups.
Among the 300 incidents of alleged torture by law enforcement agencies, which include police and elite security force Rapid Action Battalion, 123 relate to persons allegedly tortured to death in custody.
Findings of the interviews revealed the use of extreme forms of physical violence during arrest or in custody, such as kneecapping, breaking bones, drilling holes in arms and legs, or eye-gouging.
The report came as UN Committee Against Torture is about to review Bangladesh for the first time in 20 years since the country ratified the Convention Against Torture.
The UN committee's ongoing meeting that began July 22 in Geneva is to review the human rights situation in Bangladesh, Greece, Poland, and Togo under the Convention against Torture.
"Despite it having ratified the United Nations Convention Against Torture in 1998, Bangladesh has a dismal record, with torture a common practice that disproportionately affects the most vulnerable members of society," said OMCT Secretary General Gerald Staberock in statement.
"Torture is used to instil fear and quash dissent, to coerce confessions or as a routine tool for corrupt law enforcement agents to extract bribes. Impunity for perpetrators reigns supreme, further reinforcing these abhorrent practices."
The government dismissed the report as baseless.
"Law and order situation in Bangladesh is now very good. This report is baseless. These are the propaganda of a coordinated group against Bangladesh," said Bangladesh Home Minister Asaduzzaman Khan.
Mizanur Rahman, a Deputy Director of Rapid Action Battalion, said there was "no scope of any torture under the custody of" the force.
"We are aware of the rights of every individual and we always act within a legal framework," he said.
( With inputs from IANS )