Relations between the two regional powers are already broadly strained by the Syrian civil war and the rise of Isis.
Turkey's parliament voted last week to extend its military presence in Iraq for a further year to take on what it called “terrorist organisations” – a likely reference to Kurdish rebels as well as Isis.
Iraq's parliament responded on Tuesday night by condemning the vote and calling for Turkey to pull its estimated 2,000 troops out of areas across northern Iraq.
“We have asked the Turkish side more than once not to intervene in Iraqi matters and I fear the Turkish adventure could turn into a regional war,” Mr Abadi warned in comments broadcast on state TV on Wednesday.
“The Turkish leadership's behaviour is not acceptable and we don't want to get into a military confrontation with Turkey.”
Turkey says its military is in Iraq at the invitation of Masoud Barzani, president of the Kurdish regional government, with which Ankara maintains solid ties. Most of the troops are at a base in Bashiqa, north of Mosul, where they are helping to train Iraqi Kurdish peshmerga and Sunni fighters.
Turkey's deputy prime minister, Numan Kurtulmus, said the deployment had become necessary after Isis's seizure of Iraq's second city, captured in 2014
“Neither Turkey's presence in Bashiqa nor its operation right now in Syrian territory are aimed at occupying or interfering with the domestic affairs of these countries.”
Iraq's central government in Baghdad says it never invited such a force and considers the Turkish troops occupiers.
Tensions between Iraq and Turkey have risen with expectations of an offensive by Iraq and US-backed forces to retake Mosul.