Baghdad is to host a regional summit late this month, with French President Emmanuel Macron attending, the Iraqi prime minister's office said on Monday.
Iraq's Foreign Ministry said Saudi King Salman and Turkish President Recep Tayyip Erdogan had been invited, although an exact date has not been announced.
Baghdad is under pressure from powerful pro-Iran armed groups in Iraq to ensure that American personnel from a US-led coalition, which includes French troops, withdraw from the country.
Baghdad has not said whether newly inaugurated President Ebrahim Raisi of Iran would attend.
Iraq is seeking to establish itself as a mediator between Arab countries and Iran.
Mr Macron told Iraqi Prime Minister Mustafa Al Kadhimi in a phone call that he planned to visit Iraq to attend the conference, Mr Al Kadhimi's office said.
It would be Mr Macron's second visit to the country in less than a year.
Iraq, an ally of Tehran and Washington, has been an arena for bitter rivalry between the two countries.
Baghdad has this year hosted senior Iranian and Saudi officials in efforts to help Tehran and Riyadh restore their relations, which collapsed in 2016.
A rebuilding of ties between those two regional heavyweights would benefit Iraq, which regularly sees rocket attacks by pro-Iran groups against US interests, including troops sent to fight ISIS.
Iraq officially declared victory over ISIS in 2017, but 2,500 US soldiers, alongside other coalition troops, remain in the country, and the extremists continue to carry out attacks.
Several hundred French troops are in Iraq as part of the anti-ISIS coalition in both Iraq and Syria.
While Iran considers ISIS to be an enemy, it is more preoccupied with the US presence in Iraq than any risk of a resurgence by the militants.
US President Joe Biden announced in July that US combat operations in Iraq will conclude by year-end.
The presence of pro-Iran paramilitaries in Iraq is routinely used by Tehran as a bargaining chip in diplomacy with Baghdad, Iraqi officials say.
Ramzy Mardini, an associate at the Pearson Institute at the University of Chicago, said the planned regional meeting was an "important step in symbolism and reflects the co-operative ties of the prime minister to regional leaders".
But its significance "should not be overstated".
The Iraqi "state ... remains contested, internally", Mr Mardini said.
Iraq's pro-Iran armed groups regard Mr Al Kadhimi, who has faced an uphill battle in trying to contain their power, as too close to Washington.
Mr Macron "praised Iraqi diplomacy as balanced" during Monday's call, Mr Al Kadhimi's office said.