Islamic State has warned of repeated attacks in Bangladesh and beyond until rule by sharia, Islamic law, is established, saying in a video last week's killing of 20 people in a Dhaka cafe was merely a glimpse of what is to come.

Five Bangladesh militants, most from wealthy, liberal families, stormed the upmarket restaurant on Friday and murdered customers, the majority of them foreigners, from Italy, Japan, India and the United States, before they were gunned down.

"What you witnessed in Bangladesh ... was a glimpse. This will repeat, repeat and repeat until you lose and we win and the sharia is established throughout the world," said a man identified as Bangladeshi fighter Abu Issa al-Bengali, in the video monitored by SITE intelligence site.

Bangladesh has rejected the Islamic State's claim of responsibility for the Friday attack and blamed it on a domestic militant group.

It was one of the deadliest attacks in Bangladesh, where Islamic State and al Qaeda have claimed a series of killings of liberals and members of religious minorities in the past year. The government has also dismissed those claims.

The IS video began with pictures of recent attacks in Paris, Brussels and Orlando in the United States that the Middle East-based militants have claimed.

The fighter in the video, who spoke in both Bengali and English, said Bangladesh must know that it was now part of a bigger battlefield to establish the cross-border "caliphate" the group proclaimed in 2014.

"I want to tell the rulers of Bangladesh that the jihad you see today is not the same that you knew in the past," he said from a busy street in the militant group's de facto capital of Raqqa, in Syria.

"The jihad that is waged today is a jihad under the shade of the Caliphate."

Though Bangladesh has rejected the IS claim of responsibility for Friday's attack, police said they were stepping up security in response to the video threat.

"We are taking this issue seriously. All our concerned units are working tirelessly," said deputy police inspector general Shahidur Rahman.

Police believe the domestic Jamaat-ul-Mujahideen Bangladesh, which has pledged allegiance to Islamic State, played a significant role in organizing the band of privileged, educated young men who carried out the attack.

Police have said they are hunting for six members of the group suspected to have helped the attackers.

But foreign security experts say the scale and sophistication of the attack on the Holey Artisan bakery cafe pointed to some level of guidance from international militant groups.

Officials in Dhaka said on Tuesday police commandos had mistakenly shot dead a restaurant chef during the operation to end the siege.

H.T. Imam, a political adviser to Prime Minister Sheikh Hasina, also said security officials had seen online warnings about an impending attack on Friday and ordered major hotels and restaurants in the neighborhood of the cafe shut.

But they missed the actual target, he said.