Iraq announced on Wednesday it had seized five top Islamic State group commanders, after an intelligence operation lured the fighters - including a close aide of the group's leader - across the border, according to state TV.
Hashimi referred to Eithawi and Jamal as "the two most senior Islamic State figures ever to be captured alive".
Following the airstrike, the paper reports, USA and Iraqi agents persuaded al-Ithawi to help set a trap and convince the other ISIS leaders to leave Syria and enter Iraq.
Originally from Iraq, Baghdadi has been dubbed the "most wanted man on the planet" and the United States is offering a $25 million reward for his capture.
They were named as Saddam al-Jammel, Mohammed al-Qadeer, Ismail al-Eithawi, Omar al-Karbouli and Essam al-Zawbai.
An Iraqi rapid response forces member walks past a wall painted with the flag commonly used by ISIS, in Mosul, January 8, 2017.
Last year, the Pentagon said that there were "some indicators" that al-Baghdadi was still alive a month after Russian Federation claimed to have killed him in a strike near the Syrian city of Raqqa.
Iraqi and U.S. intelligence spent several weeks interrogating Abu Zeid to acquire information about the location of the other leaders, who were in hiding.
Iraqi Prime Minister Haider al-Abadi said last month he would "take all necessary measures" against militants based in Syria. But the militants still pose a threat along the border with Syria and have continued to carry out ambushes, killings and bombings across Iraq. At the height of the group's power their self-proclaimed caliphate stretched from the edges of Aleppo in Syria to just north of the Iraqi capital, Baghdad.