Police say they have arrested four suspects in last month's killing of an Italian citizen in the Bangladeshi capital.

Italian aid worker Cesare Tavella was gunned down by motorcycle-riding assailants while jogging on the streets of the Dhaka's diplomatic quarter.

Responsibility for the attack was claimed by the Islamic State group, but the Bangladeshi government denied the extremist Sunni militant group had any presence in the impoverished South Asian nation.

Dhaka Metropolitan Police Commissioner Asaduzzaman Mia told reporters on Monday that authorities had arrested three men suspected of carrying out the killing, as well as the owner of a motorcycle suspected of being used in the attack.

Mia said the suspects said they were hired by "a big brother" to kill Tavella to "create chaos" in the country.