The attack came just before 3:30 a.m. local time and caused only minor damage.
The plan is for NATO to take on some personnel and training activities now run by the US-led multinational coalition.
Esper is looking for ways to reduce the U.S. troop presence in Iraq so that some can be brought home.
Some of those affected are close relatives of refugees who are already in the U.S.
The latest figures represent a dramatic increase from the last Pentagon injury report.
Officially, Iraqis have been unclear on the status of joint operations.
The U.S. has yet to receive assurances from Baghdad that the Patriot would be allowed into the country.
Gen. McKenzie became the most senior military official to visit since an U.S. drone strike killed a top Iranian general.
More than 60 troops who suffered TBI from the Iranian missile strikes are likely to be approved for Purple Hearts.
Ali Yousif Ahmed Al-Nourihad shot and killed a lieutenant and an officer with the Fallujah Police Directorate in 2006.