Mr Kamilov told a news conference that the suspect had «actively urged his compatriots to travel to Syria in order to fight for IS». Mr Akilov had used online messaging services, he said.
Earlier, an Uzbek security source quoted by the Reuters news agency said Mr Akilov himself had tried to travel to Syria in 2015 to fight for IS. However, he was stopped on the Turkey-Syria border and was sent back to Sweden.
No group has claimed to be behind the Stockholm attack.
Mr Akilov reportedly ran from the scene of the attack, still covered in blood and glass, and was arrested later in a northern suburb of Stockholm.
According to reports, he had left a wife and four children behind in Uzbekistan in order to earn money to send home.