Home Minister Asaduzzaman Khan rejected the report, saying police were only shooting at criminals as a "last resort".
The 45-page report quoted victims recounting how they had been shot without provocation by police officers who then claimed that they had opened fire in self-defence.
"Security forces in Bangladesh have long killed detainees in fake 'crossfire killings', pretending the victim was killed when the authorities took him back to the scene of the crime and were attacked by one of his accomplices," said Brad Adams, Asia director of HRW.
The New York-based group called on Prime Minister Sheikh Hasina's government to invite the UN rights office and UN special rapporteurs on torture and extrajudicial executions to investigate the "kneecappings" and other alleged acts of torture.
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HRW said its report includes evidence and testimony from 25 individuals, mostly members and supporters of the main opposition Bangladesh Nationalist Party (BNP) and its Islamist ally Jamaat-e-Islami.
Several of the victims have been permanently disabled, including some who had their legs amputated after being shot, it said.
"This is not true," Khan told AFP.
He added that security forces had only shot at "criminals" when they "try to escape" or were in confrontation with police.
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