A Bangladeshi-Canadian was on Saturday identified as the mastermind of Bangladesh's worst terror attack at a cafe in Dhaka.

The slain militants are believed to be members of Jamatul Mujahideen Bangladesh.

An intelligence agency of a foreign country mobilsed funds for the Dhaka cafe attack which was carried out on behalf of a top fundamentalist Jamaat-e-Islami leader who is on death row after being convicted for 1971 war crimes in Bangladesh, according to a media report.

Three Islamists from the infamous Al-badr militia were on Monday sentenced to death while five others jailed until death by a special tribunal in Bangladesh for committing crimes against humanity during the 1971 liberation war against Pakistan.

"Our initial investigation suggests both the attacks were carried out by homegrown Jamaatul Mujahideen Bangladesh," said the home minister.

Britain and Canada have already banned Naik from visiting several years ago.

"The five terrorists killed at Gulshan (cafe) were JMB members. The police had their details and been looking for them for a while," Inspector General of Police AKM Shahidul Haque told media persons.

Bangladesh on Tuesday pressed anti-terrorism charges against several suspects and identified the fifth assailant in the country's worst terror attack as authorities intensified efforts to unravel the plot behind the brazen assault in which 22 people were slaughtered by Islamists.

'My son used to pray five times a day from a young age. But we never imagined this. There was nothing at home, no books or anything to indicate he was leaning that way, So we had no inkling,' he said.

Inspector General of Police AKM Shahidul Haque, however, did not disclose the identities of either of the detainees or where they were being kept.

The Bangladesh government on Sunday claimed the attackers who slaughtered 20 hostages inside a cafe in Dhaka in the country's worst terror attack were members of "homegrown" Islamist terrorist outfits and not Islamic State of Syria and Iraq militants.

All the hostages killed during the 12-hour siege by Islamic State terrorists were foreigners, with most being Italian or Japanese.

Condemning the attack, Bangladesh Prime Minister Sheikh Hasina said, "What kind of humans are these, who are killing other humans during (the holy month of) Ramzan? They don't have any religion."

Shymanondo Das, in his mid 50s, was hacked by three motorcycle-borne assailants when he was plucking flowers for morning prayers at a garden in the Radhamodon Gopal Moth premises in Jhenaidah, said Jbahar Ali Sheikh, additional superintendent of police in Jhenidah.

He said the militant was killed in a pre-dawn encounter in Dhaka and was named in a police list as Shariful or Sharif, but he previously used several other names like Sakib alias Saleh alias Arif alias Hadi-1.

With a wind speed of up to kilometres per hour while heading east-northeastward, the cyclone hit the Barisal-Chittagong region, sending impacts across the country.

58-year-old doctor Sanaur Rahman was riding home on his motorbike when he was attacked by machete-wielding militants in Kushtia town.

A Hindu tailor was hacked to death by machete-wielding Islamic State militants in his shop on Saturday in central Bangladesh.

Rajshahi University professor AFM Rezaul Karim Siddiquee, 58, was murdered within 50 metres of his residence in the country's northwestern city of Rajshahi, police said.

This operation was conducted to teach a lesson to the blasphemers of this land whose poisonous tongues are constantly abusing Allah...the religion of Islam and the Messenger...under the pretext of so-called 'freedom of speech', Mufti Abdullah Ashraf, a spokesman for Ansar al-Islam, said in the statement according to SITE Intelligence Group.