As part of their push for a change in the law, the Hefajat-e-Islam organisation on Monday forced the closure of schools and businesses across the country as part of a general strike.
And television reports said scores of people had been injured in clashes between pro-government activists and Islamists, already infuriated by the recent convictions of leading opposition figures for war crimes.
But Sheikh Hasina, who has been leading a secular government in the Muslim-majority country since 2009, said existing laws were adequate to prosecute anyone accused of insulting a religion.
“Actually, we don’t have any plan to (bring in a new law). We don’t need it,” Hasina told the BBC in an interview broadcast Monday.
“They should know that existing laws are enough,” she added, before stressing that “this country is a secular democracy”.
On Saturday hundreds of thousands of Islamists rallied in the capital Dhaka to demand a blasphemy law, with provisions for the death penalty for those who defame Islam.
There has been vociferous debate between staunch atheists and fundamentalists in Bangladesh’s social media for years, but it took a deadly turn in February when an anti-Islam blogger was murdered.
Four online writers were arrested last week on charges of hurting religious sentiment through their Internet writings against Islam.
Under existing cyber laws, anyone convicted of defaming a religion on the Internet can be jailed for up to 10 years.
Hefajat-e-Islam, which describes itself as a non-political organisation, has given the government until the end of the month to meet a series of demands or face a blockade of the capital.
The group also wants Islamic education to be made mandatory in primary and secondary schools, members of the Ahmadi sect to be declared non-Muslims and the restoration of pledges to Allah in the constitution, which Hasina’s government has deleted.
Hardline Islamist groups have accused Hasina’s government of trying to intimidate the opposition through a series of trials for war crimes allegedly committed during the 1971 war of independence.
Three Islamists have so far been convicted and two of them were sentenced to death. At least 96 people have been killed during protests over the trials since January.