Independently of Washington, Tehran has poured significant resources into the war against the jihadists in Iran...
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.
Its involvement has irked Washington but has been fiercely defended by the Iraqi prime minister, who gave a firm rebuff to US Secretary of State Rex Tillerson over his comments on the issue when he visited Baghdad on Monday.
Abadi held talks with Iran's supreme leader Ayatollah Ali Khamenei and with President Hassan Rouhani.
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.
Abadi has been deeply defensive of his government's close alliance with neighbouring Iran, which like Iraq is a Shiite-majority country.
When Tillerson visited Tehran's Sunni arch rival Riyadh on Sunday and called for Iranian militias in Iraq to "go home" as the fight against IS was coming to a close, he earned a sharp rebuke from Abadi.
"The fighters of the Hashed al-Shaabi are Iraqis who have fought terrorism, defended their country and made sacrifices to defeat (IS)," Abadi said, according to a statement from his office.
The 60,000-strong Hashed was formed in 2014 after IS seized swathes of northern and western Iraq, routing government forces.
A paramilitary force mostly made up of Iranian-backed militias, it has played a key role in Iraq's successful fight against the jihadists over the past three years.