The suspected mustard gas attack on Taza that left a three-year-old girl dead "will not go unpunished", the premier said in a statement.
A large number of rockets were fired at Taza on Wednesday from the nearby village of Bashir, which is held by the extremists.
Intelligence experts are still analysing samples, but local officials believe mustard agent was used in the attack on Taza, which lies just south of the city of Kirkuk and is around 220 kilometres (135 miles) north of Baghdad.
CIA director says IS group has used, can make chem weapons
Abadi promised that medical support would be provided to the town, where hundreds of people were treated following the chemical attack.
Iranian Health Minister Hassan Hashemi said Saturday a medical team from the Islamic republic had arrived in Kirkuk after an "urgent request" from his Iraqi counterpart, Iran's ISNA news agency reported.
Hundreds of people attended the funeral on Friday of Fatima Samir, the girl who died of wounds suffered in the attack. Some of the mourners carried placards demanding protection.
The Iraqi air force carried out a strike on Bashir overnight and Abadi promised a ground operation to retake the village from IS soon, pro-government militia commander Abu Ridha al-Najjar said.
Radioactive material stolen in Iraq raises security fears
Bashir lies in an area that is officially under federal administration but is controlled by Kurdish forces that de facto expanded their autonomous region on the back of the exremists’ 2014 offensive.
Tension has been high between Kurdish forces and Shia militias in the area, impeding military cooperation against IS.
In February, US Director of National Intelligence James Clapper and CIA Director John Brennan for the first time openly accused IS of using chemical weapons, including mustard gas, in Iraq and Syria.
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