As part of their push for a change in the law, the Hefajat-e-Islam group on Monday forced the closure of schools and businesses and barricaded inter-city motorways and railways across the country in a general strike.
Police said at least 30 people were injured in clashes between pro-government activists and Islamic groups, 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 protesters 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.
Hasina said her government would "go through all the demands" to see "if there is any reasonable one" which it could act on.
Her party, however, accused Hefajat, which draws its support from the country's tens of thousands of Islamic seminaries, of being a pawn of the opposition.
Wielding sticks, thousands of Hefajat activists clashed with ruling Awami League activists in the port city of Chittagong and northern city of Mymensingh as they barricaded roads and inter-city highways.
At least 30 people including five policemen were injured in the clashes, local police chiefs told AFP, adding they fired tear gas and blank shots to disperse the protesters.
About 2,000 protesters also barricaded a railway in the eastern Brahmanbaria district, halting trains between the capital Dhaka and Chittagong for about four hours, local police chief M Moniruzzaman told AFP.
Hardline 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 people 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.
COMMENTS (9)
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ
Just to make things clear, no country can be a "secular democracy" while having laws where people can go to prison just for speaking their mind regardless the subject. If anything, they need to eliminate these laws, not introduce stricter ones.
Best of luck to the honorable Prime Minister of Bangladesh, she has really got the backbone. May Allah be with her. Ameen.
@Yoghurt lover, clearly an influence of Pakistan? So now everything that happens in Bangladesh is an influence of Pakistan, thats like the US saying "all of our ills are clearly an influence of the British", Bangladesh has been an independant state for 40 years nothing there is an influence of Pakistan, anymore.
This is clearly an influence of Pakistan.
Good on Sheikh Hasina to resist such fundamentalist demands.
But this also poses a bigger danger. The moment Mrs. Zia comes to power, she will do everything in her power to appease the Islamists and to simply irritate Hasina.
Khalida Zia should not become the Zia-ul-haq of Bangladesh.
@Rex Minor: " so called genocide."
So called genocide? Even Sharmila whom all Pakistanis love to quote says that over 200,000 Bengalis were killed.
I like her . she has done a good thing by not bowing to fanatics by imposing more laws on religion .
Haseena is on the verge of loosing her title of Sheikha with a fatwa that she is an Atheist! The military or police cannot protect her rule of law where the majorities do not feel protected while her policy of vengence against the suspects of 1971 so called genocide.
Rex Minor
Good for Bangladesh. Hope it stays that way.
Bangladesh’s prime minister has ruled out a new blasphemy law despite a mass campaign by Islamic groups to introduce the death penalty for bloggers . Pakistani politicians should take note -- standing up to the extremist can be done - it just takes a backbone.