"With the instructions of the home ministry and in aid of the civil administration, required number of BGB has been deployed in different districts of the country," lieutenant colonel Fayzur Rahman told AFP, without disclosing the numbers involved.
Rahman, who is the operations director of the force, said there had been no reports of violence after their deployment.
"Situation is normal," he said.
The disturbances came as Bangladesh marked 50 years of independence with rights groups calling for an end to growing authoritarianism including forced disappearances and extra-judicial killings.
Police said four bodies of members of Hefazat-e-Islam, a hardline Islamist group, were brought to Chittagong Medical College Hospital after violence erupted at Hathazari, a rural town where the group's main leaders are based.
A supporter of the group was also killed in clashes in the eastern border town of Brahmanbaria, another key bastion of Hefazat.
A Hefazat spokesman said tens of thousands of supporters of the group demonstrated on Friday to protest against Modi's two-day tour to Bangladesh.
The group has also called nationwide demonstrations for Saturday and a strike on Sunday to protest against the police's actions and firing on "peaceful" protesters.
Hefazat is known for its nationwide network and large-scale protests demanding Bangladesh introduce blasphemy laws.
In 2013 police clashed with tens of thousands of Hefazat supporters in Dhaka, leaving nearly 50 people dead.
Hefazat aside, a diverse range of Bangladeshi groups -- including students, leftists and other Islamist outfits -- have been staging protests against Modi's visit.
They accuse Modi and his Hindu-nationalist government of stoking religious tensions and inciting anti-Muslim violence including in the Indian state of Gujarat in 2002 when 1,000 people died. Modi was Gujarat's chief minister at the time.
Modi was set to visit two key Hindu temples in rural districts of southern Bangladesh on Saturday.
As protests spread, Facebook users complained they could not access the site.
Post and telecommunications minister Mustafa Jabbar said his ministry was not responsible for the stoppage.
"This is not our decision," he told AFP, adding it was up to the law enforcement agencies to say what actions they had taken.
"We're aware that our services have been restricted in Bangladesh. We're working to understand more and hope to have full access restored as soon as possible," a Facebook spokesperson said.