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Independently of Washington, Tehran has poured significant resources into the war against the jihadists in Iraq, providing weapons, advice and training to the Shiite militias which dominate the key paramilitary Hashed al-Shaabi (Popular Mobilisation) force.
Abadi held morning talks with First Vice President Eshagh Jahangiri ahead of meetings with other top leaders.
Buoyed by the success of the campaign against the jihadists, who have now been virtually confined to a stretch of the Euphrates valley straddling the border with Syria, Abadi has been on a regional tour that on Wednesday saw him in Ankara.
High on the agenda of his talks has been his bitter dispute with the Kurds over the spoils of the fightback against IS.
Kurdish leaders held a referendum on independence last month to the fury not only of Baghdad but also of neighbouring Iran and Turkey which have long been fearful of anything that might stoke separatist sentiment among their own large Kurdish minorities.
In a statement issued by his office in Baghdad on Thursday, Abadi said that an offer by Kurdish leaders to freeze the outcome of the vote did not go far enough. He said only complete annulment would suffice.