Abadi insisted no Turkish involvement was wanted following a meeting with US Defence Secretary Ashton Carter, who was in Baghdad Saturday to review progress in the six-day-old offensive.
"I know that the Turks want to participate... We tell them 'thank you, this is something the Iraqis will handle and the Iraqis will liberate Mosul'," Abadi said.
UN 'extremely concerned' for 1.5 million civilians in Mosul
"We don't have any problems. If we need help, we will ask for it from Turkey or from other countries in the region," he said.
Carter visited NATO member Turkey on Friday and suggested he could see a role for Turkey in the Mosul operation.
The United States has been a key supporter of Abadi and Iraq's military operations to reconquer the swathes of land lost to IS militants in 2014.
It heads a 60-nation coalition that has carried out thousands of air strikes against IS targets, has trained thousands of Iraqi forces and is advising them on the ground.
US tries to defuse Iraq-Turkey war of words over Mosul
Turkey has a base in northern Iraq and is in fact already involved on the ground in the north of the country, but Abadi is under popular pressure to publicly reject Ankara's presence.
Key components of the government in Baghdad have accused Ankara of abetting the Islamic State group that once controlled more than a third of Iraq.
On October 17, Abadi announced the start of a huge offensive to retake Mosul, Iraq's second city and the last major extremists stronghold in the country.
Besides being Iraq's biggest military operation in years, the offensive is also extremely complex, owing to the large numbers of ethnic and religious groups in northern Iraq, many of which are backed by Turkey or Iran.
Turkish President Recep Tayyip Erdogan has made it clear he wanted his forces to play an active part in the Mosul offensive.
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