"The president of the republic asked for everything possible to be done to avoid conflict between Iraqis and that, within the limits of the unity of Iraq and its constitution, a dialogue taking account of the rights of the Kurds and the minorities should be held between [the Iraqi Kurdish capital] Erbil and Baghdad," a statement by the Elysée presidential palace said.
After Iraqi Kurds voted for independence for their region in a referendum Baghdad declared illegal, central government troops have seized the oil-rich province of Kirkuk and much of Nineveh province from Kurdish peshmerga forces.
Macron welcomed the establishment of a committee to discuss joint deployment of Kurdish and Iraqi federal forces in the disputed areas, the statement said.
The clashes have come after a successful offensive captured most of the territory seized by IS over the last three years.
Macron and al-Abadi both "confirmed the importance of the struggle still going on in Iraqi soil to chase Daesh [IS] from all Iraqi territory with the help of the international coalition in which France is playing a full role", the Elysée statement said.