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.
Turkey has said the campaign will send a wave of refugees over its border and, potentially, on to Europe.
Ankara worries that Baghdad's Shi'ite Muslim-led forces will destabilise Mosul's largely Sunni population and worsen ethnic strife across the region, where there are also populations of Turkmens, ethnic kin of the Turks.
Turkey is also uncomfortable with the arrangement of Kurdish forces expected to take part in the offensive.
In northern Syria, where Turkey is backing rebels fighting Islamic State, Ankara has warned that Kurdish militias are “filling the vacuum” left by Islamic State. Fearing that this will boost the Kurdish rebellion across the border in southeast Turkey, it has threatened to “cleanse” them.
Turkey announced late on Tuesday that it was summoning Iraq's ambassador to complain about the parliamentary vote.
“We believe this decision does not reflect the views of the majority of Iraqi people, whom Turkey has stood by for years and attempted to support with all its resources,” Turkey's Foreign Ministry said.
“We find it noteworthy that the Iraqi parliament, which has not said anything about the accepted mandate for years, puts this on the agenda as though it were a new development in times when terror is taking so many lives in Turkey and Iraq.”
On Wednesday, Iraq summoned the Turkish ambassador to Baghdad to protest what it said were “provocative” comments from Ankara about the troop deployment.