Prime Minister Sheikh Hasina said in an exclusive interview with the BBC that sufficient laws are in place to punish people who insult any religion, not just those who defame Islam and Prophet Muhammad.
"This country is a secular democracy. So each and every religion has the right to practice their religion freely and fair," she told the BBC.
"But it isn't fair to hurt anybody's religious feeling. Always we try to protect every religious sentiment."
Her comments come as members of the religious group Hefajat-e Islam continue to march through the capital urging a nationwide shutdown of businesses and demanding tougher blasphemy laws including use of the death penalty.
Among their demands is strict punishment of so-called atheist bloggers whom they blaspheme Islam and Prophet Muhammad, a report by the Daily News said.
"A new law will have to be formulated incorporating the provision of the punishment suggested in Islam," Noor Hossain Kashemi, leader of the Dhaka city branch of Hefajat, said.
Kashemi claimed that one member of Hefajat-e Islam was shot dead by police in Chittagong and more than 400 Hefajat men were injured across the country when attacked by members of the ruling Awami League party, in power since elections in January 2009.
He also apologized for attacks by his members on two reporters and two cameramen -- one of them a woman.
"On behalf of our leaders we express regret to the journalists who were injured by our men mistakenly," Kashemi said.
The Financial Express newspaper reported that Hefajat-e Islam said it will close down Dhaka May 5 if the government doesn't act upon the religious group's demands.
During the BBC interview, the prime minister said her government would consider their demands but wouldn't make promises about fulfilling the group's wishes.
"We will go through all the demands and then we will see," Hasina said.
"If there is any reasonable one, we will fulfil it. If it isn't reasonable or isn't suitable for our country or society we won't accept it."
Hasina also defended the arrest of four bloggers last week on suspicion of harming religious sentiment through their work, saying the government "can take any action" to protect society.
Eight blog operators blacked out their websites in protest.
The prime minister also rejected calls by the main opposition Bangladesh Nationalist Party to restore a neutral interim caretaker administration to oversee parliamentary polls.
The BNP said it will boycott an election because the process wouldn't be free and fair.
"If they don't participate in the election, as a political party they will lose their seats," Hasina told the BBC.
The Financial Express newspaper reported that several members of BNP attended protest rallies on the weekend and told the crowd they had solidarity with the program of Hefajat-e-Islam.
Notable deaths of 2014 [PHOTOS]