"We have arrested the four - two of them actively took part in the killing of Cesare Tavella - we will let you know the details later," a police spokesman told PTI.
The official said all the four were tracked down from different areas of the capital after a thorough investigation.
Tavella, 50, was shot thrice from a close range on September 28 while he was jogging. Five days later, a 66-year-old Japanese farmer was also killed by unidentified assailants in a similar attack on the outskirts of northern Rangpur city sparking an international uproar.
But the development came a day after Home Minister Asaduzzaman Khan Kamal said that all the three incidents were interlinked with same group of people masterminding the attacks while investigators nearly tracked down the culprits.
Also Read
"Give us just one or two days and by that time we expect the real culprits to be exposed to justice," he said.
"The (reported IS) claim is entirely baseless and Islamist militants were not involved in it...(but) the same group of people masterminded the attack to create instability and discredit our (ruling Awami League) government," he said.
"The motorbike owner is one of the four who has been arrested today," a police officer said.
The Islamic State has claimed responsibility for the murders and attack on Shiites in Dhaka.
Bangladesh, a Muslim-majority country, has been rocked by gruesome murders of atheist bloggers this year. The attacks have sparked a crackdown on hardline Islamist groups.