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8 year oldExplosions and heavy gunfire were heard in the area around the Holey Artisan Bakery cafe. At least eight hostages were rescued, police say. The fate of the others is unknown.
Several of those held are believed to be Italian, and some may be Japanese.
The militant group Islamic State (IS) has said it carried out the attack.
"Intense gunfighting (is) on," Mizanur Rahman Bhuiyan, of the Rapid Action Battalion force, told Reuters after the rescue operation was launched on Saturday morning.
Later reports said the gunfire stopped.
At least two police officers were killed in earlier exchanges of fire late on Friday, and 30 police officers have been injured.
Officials told the BBC that said army and navy commandos were leading the operation, along with police and the paramilitary Border Guards Bangladesh.
Armoured vehicles were also seen moving towards the cafe.
People from the Gulshan neighbourhood where the cafe is located said they had heard gunshots, after hundreds of soldiers approached the building.
Eight or nine armed men burst into the cafe in the diplomatic area of the city at about 21:20 (13:20 GMT) on Friday and opened fire.
A statement on the IS self-styled news agency Amaq said militants had attacked a restaurant "frequented by foreigners". It said that more than 20 people "of different nationalities" had been killed but this has not been confirmed.
Seven Italian nationals are believed to be in the cafe, the Italian ambassador in Dhaka, Mario Palma, was quoted as saying by Italian media.
A Japanese government spokesman said Tokyo was investigating reports that some of its citizens were among the hostages.
The attack comes after a spate of murders of secular bloggers, gay activists, academics and members of religious minorities, blamed on Islamist militants.
This is probably the first time ever foreigners have been taken hostages in Bangladesh.
Though there have been a number of killings focusing on academics, activists and member of religious minorities, attacks on foreigners are rare.
The timing is important. Bangladesh has been gearing up for the Muslim religious festival of Eid, and most people have started going to their homes in villages and towns across the country for a week-long holiday period.
The government has always denied the presence of Islamic State militant group in Bangladesh.
So far the militants have targeted individuals and sometimes security forces. But storming a cafe in a heavily guarded diplomatic district is unprecedented and a dramatic escalation in violence.
The government has been caught unaware, and the attack exposes a big hole in Bangladesh's intelligence gathering and security system.
The cafe is described as being popular with expatriates, diplomats and middle-class families.
Media reports quoted witnesses as saying that "Allahu Akbar", meaning "God is greatest", was heard as the militants entered the cafe.
BBC South Asia editor Jill McGivering says that although high-profile gun attacks are rare in Bangladesh, the latest incident follows a series of murders widely blamed on Islamist extremists.
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