Militants of the extremist Islamic State group have been barreling through the area for the past three days.
Al-Maqdisi was the mentor of Abu Musab al-Zarqawi, the leader of al-Qaida.
French President Francois Hollande announced that the target was “entirely destroyed”.
The military action will end only when they have ended the capacity of ISIL to engage in broad-based terrorist activity.
“It’s a very dangerous phenomenon, and we all need to be aware of how to deal with this issue,” said Iran FM.
Obama’s message came a day after knowing about a possibility of some ground forces during congressional testimony that worried some Democrats.
The slick 52-second video entitled “Flames of War” shows militants blowing up tanks and images of wounded US soldiers.
The comprehensive approach to degrade and ultimately destroy ISIL requires a wide range of efforts, said Obama.
While the rhetoric against the ISIS has been consistent across the globe, their name hasn’t.
Several important tests loom for the U.S. administration’s nascent coalition to “degrade and defeat” the ultra-hardline Islamic State.
“I saw no point in cooperating with a country whose hands are dirty and intentions murky,” said Ayatollah.
US Secretary of State John Kerry ruled out any military coordination with Iran, which in the end was not invited to Paris.
“The air strike southwest of Baghdad was the first strike taken as part of our expanded efforts beyond protecting our own people,” said US.
The Obama administration says the training operation is needed to establish credible, local ground forces to accompany U.S. air strikes.
U.S. Secretary of State John Kerry has been pressuring allies to show a united front to defeat the militants.