"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.
A Dhaka court on Monday placed three of the four suspects on an eight-day remand.
Metropolitan Magistrate Mohammad Mahbubur Rahman passed the order after Inspector Zehad Hossain of Detective Branch of Dhaka police produced the suspects before him seeking their remand.
The Tavella murder suspects confessed to being hired for killing "a white man" to create anarchy in the country, Dhaka Metropolitan Police Commissioner Mohammad Asaduzzaman Miah said.
"Not Tavella, they were contracted to kill any foreign national especially a white-skinned man," the DMP chief was quoted as saying by the Daily Star.
The attacks on the foreigners was claimed by the Islamic State. Two days ago, unknown miscreants carried out an unprecedented attack with improvised grenades on a Shiite procession in the old part of Dhaka. This attack was also claimed by the Islamic State.
However, Home Minister Asaduzzaman Khan Kamal on Sunday said that all the three incidents were interlinked with same group of people masterminding the attacks.
"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.
Tavella was the project manager of a Netherlands-based NGO who was gunned down in the high-security diplomati
Gulshan area while police said two men actively took part in the killing while a third man waited nearby on a motorbike to take the assailants to safety.
"The motorbike owner is one of the four who has been arrested today," a police officer said.
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.