It has also emerged that one of the dead gunmen was the son of a governing party politician.
The so-called Islamic State (IS) group said it was behind the attack in Dhaka, but the government has denied this.
The man previously believed to be a hostage was detained after footage of the assault filmed by eyewitnesses from nearby buildings showed he could be linked to the attackers, police said.
The politician`s son had been reported missing by his parents after he disappeared in December.
They recognised him from photographs of the attackers published in local media.
Bangladeshi officials have named five of the men and said they belonged to a local banned militant group.
"They are members of the Jamaeytul Mujahdeen Bangladesh (JMB)," Home Minister Asaduzzaman Khan said. "They have no connections with the Islamic State."
However, IS earlier released photographs of the alleged attackers posing in front of a black IS flag.
Mr Khan said the men had made no demands during the attack. He said three of the gunmen were under 22 and had been missing for six months.
They are said to belong to affluent families and had studied in elite private schools and universities, not in Islamic seminaries or madrassas where many Islamist militant groups are thought to draw recruits.
Police chief Shahidul Hoque made some of the men`s first names public: Akash, Bikash, Don, Bandhon and Ripon.
More about:
-1780923278.jpg&h=190&w=280&zc=1&q=100)
