There is no U.S. involvement in the Tikrit offensive and U.S. officials have said the Iraqis have not requested airstrikes to support the operation.
Al-Abadi acknowledged that Soleimani “comes and goes” to Iraq, but that he does not stay long.
"He just comes for a visit and he goes," he said.
Al-Abadi added that he had not personally seen Soleimani during a visit earlier this week to Samarra in Saladin Province, close to the fighting.
Al-Abadi said it was “not entirely true” that American military commanders did not know beforehand that the Iraqi military was launching the Tikrit offensive, noting that the U.S. and Iraqi military coordinate plans at a Baghdad Joint Operations Center.
“I know probably some are surprised and unhappy in - in Washington - because they haven't taken a full control over these operations,” he said. “We have to take charge of what we are doing because it's Iraqi lives which has been sacrificed.”
Al-Abadi claimed the U.S. does not see the Iranian help as a problem as the Iraqis have “the right to use all capabilities available to defend our own forces, our own land.”
The U.S. currently has 2,600 military personnel in Iraq to advise and train Iraq’s military, but al-Abadi did not expect them to someday be needed in combat operations.
“It doesn't help whether I wish or not. I don't think that's going to happen,” he said. “This administration and I understand the U.S. public are not eager - or they don't want to - send their own sons and troops outside [the] U.S.”
Though he expects an Iraqi offensive on Mosul to take place in early summer "just to repay the people," al-Abadi acknowledged it could be delayed. He was unable to describe how Iraqis live in areas controlled by ISIS, only saying it was "very rough."
"That's why we are very eager to liberate these areas as soon as possible," al-Abadi said.
But al-Abadi also wants an offensive to take place when Iraq’s military has received enough training and has access to supply routes and air cover.
“Our timetable is not only time-linked, it's factual-linked,” he said. “We have to achieve certain things on the ground before we can take back Mosul.”
Al-Abadi believes that taking Mosul from ISIS could deal a fatal blow to the terror group and its symbolic claims that it has established a caliphate.
“This is the center of their state," he said. "We would have killed their own ambition to establish that state on the other countries, as well, in the region."