Abadi's comments came in a wide-ranging interview Tuesday about the Kurdish referendum on independence last month, his decision to send troops into areas disputed by his government and the Kurds, and the anticipated post-Islamic State era.
The prime minister said the United States has begun to draw down its military presence in the country from its peak of 5,200 troops since the battle against the Islamic State began. He said that U.S. air power won't be needed after the Islamic State is defeated in an area in western Iraq along the Syrian border.
The next phase of cooperation between the two nations will be centered on sharing intelligence and training Iraqi forces to ensure that another militant group doesn't emerge and that a weakened Islamic State does not conduct devastating attacks outside its shrinking pockets in Iraq.
"They're going to cause problems somewhere else," Abadi said of the militant group. "It's not in our interest, nor in the interest of other countries in the region, for terrorists to regroup again."
The Trump administration has vowed to take a tougher stance on Iranian expansionism but has not clearly defined the U.S. role in Iraq after the Islamic State has been evicted.
Abadi, who faces elections next spring, said he envisions Iraq becoming an important security and economic partner to its regional allies. The struggle to evict the Islamic State, lasting more than three years, has decimated large cities, displaced millions and contributed to a financial crisis.
Establishing strong state institutions and dealing with neighboring countries from a position of mutual interest are the keys to rebuilding the country, he told The Washington Post, the Wall Street Journal and the Los Angeles Times.
To that end, Abadi has traveled to Saudi Arabia, Egypt and Turkey in recent days to deliver a message that Iraq is open for business. He is expected to visit Iran this week.
"Iraq is getting stronger, getting unified," Abadi said during the interview, which took place inside Baghdad's fortified Green Zone. "I think others, or the interference of others in the affairs of Iraq, will become less and less. This is a new-built confidence among Iraqis, the Iraqi national feeling, which our aim is to increase — people's attachment to their own country."
A nascent vision of Iraqi nationalism has fueled support for Abadi's tough military response to last month's Kurdish bid for independence. His supporters and even some of his critics have praised his decision to take control of territory claimed by both his government and the Kurds.
But Kurdish and some U.S. officials have questioned the role of Iranian-backed Shiite militias in the Iraqi operation, with accusations that Iran was largely in control of the decision to move in troops.
Abadi rejected that notion. He said he is sympathetic to Kurdish aspirations for independence but that their "unilateral" steps toward full autonomy was a threat to regional security. Abadi said he warned Masoud Barzani, the president of the Kurdish region, ahead of the referendum that he risked being "on the wrong side of history."
"In all honesty, I think this aspiration has been pushed back many years now," Abadi said, adding that Kurdish independence would require nationwide consensus.
That is unlikely to ever happen. Powerful Shiite militias, some with strong backing from Iran, are stridently opposed to Kurdish independence and have participated in the military campaign to reclaim disputed territories, including the oil-rich province of Kirkuk.
While the United States has supported Abadi's move on Kirkuk, it has expressed concern about the presence of Shiite militias in disputed areas. Abadi has defended the militias, which operate under the umbrella of a government-sanctioned force known as popular mobilization units, but said they must shed their sectarian political identities if they wish to remain part of the nation's security forces.
Some members of the most powerful groups, including the Badr Organization, hold ministerial posts and seats in parliament. Analysts say that a process to decouple the armed and political wings of the groups is far from making headway.
Abadi, who legally commands the popular mobilization units, has only nominal control over the most influential of the armed groups. Organizations like Badr are closer to Tehran than Baghdad and yet are well represented in Iraq's political and security institutions. Abadi said such groups must disarm if they wish to participate in politics.
Those who refuse, Abadi said, "would become outlaws. It's very clear."