"There is no reason to believe that all our achievements will be overshadowed by these heinous murders, but that is what is being attempted," Hasina told reporters at Ganabhaban, her official residence in the capital.
Describing the murders as "clearly planned and politically motivated", she said the killings were part of a conspiracy to "tarnish the image" of the government.
The BNP-Jamaat have "definitely abetted these murders in an attempt to overshadow Bangladesh's achievements", she said.
"We will take action and track down the culprits. But if we get carried away by these murders and overlook our achievements, the BNP-Jamaat conspiracy will be successful."
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Hosi Koniyo, 66, who was headed to an agriculture farm on the outskirts of northern Rangpur city in a rickshaw, was shot thrice in the chest, shoulder and hand by the unidentified assassins yesterday. He died instantly.
In a statement in Arabic language, the ISIS claimed responsibility for the attack on Koniyo, according to SITE Intelligence Group, which monitors jihadi postings online.
The ISIS had also claimed responsibility for the killing of the Italian aid worker last week in Bangladesh's capital.
A frequent visitor to Bangladesh, Koniyo had been in Rangpur for the past six months and was familiar in the neighbourhood because of his philanthropic work.
He had set up the farm, where he visited daily by a rickshaw, with help of a local businessman to grow grass for cattle.
Police detained the businessman, along with the rickshaw puller, Koniyo's landlord and another resident of the area, for questioning.
Security officials, either, have not ruled out that the ISIS could be using "local sympathisers" to carry out such attacks.