"We don't need it," Sheikh Hasina told the BBC Sunday in an exclusive interview addressing the demand. "They should know that existing laws are enough."
Reaffirming Bangladesh's stance as a secular democracy, Hasina added that "it is not fair to hurt anybody's religious feeling. Always we try to protect every religious sentiment."
Hundreds of thousands of Islamists rallied recently in Dhaka to call for the death penalty for blasphemy.
Islamists have set a three-week deadline for the government to meet their demands.
In her interview, Hasina also defended the government's decision to arrest four atheist bloggers on charges of harming religious sentiment.
She denied accusations the arrests were made to appease Islamists, BDNews24 reported.
"We amended our constitution to ensure equal rights for all our people to practice their religion," Hasina said.
Celebrity Breakups and divorces of 2014 [PHOTOS]