Graham, said on CBS' "Face the Nation" the U.S.-led war has "turned a corner," reporting that incidences of violence have plummeted.
"Sectarian violence is down by 90 percent," he said. "Our casualties are way down. We have a long way to go, but I believe the (2007 troop) surge has worked on all fronts."
Graham, a member of the Senate Armed Services Committee, traveled to Iraq with Sen. John McCain, R-Ariz., the presumptive GOP presidential nominee.
U.S. Sen. Jack Reed, also a member of the Armed Services Committee and who made a similar trip to Iraq in January, said despite some military progress, the Iraqis have yet to make considerable progress politically.
"The longer they feel we will take the lead, the longer they feel that we are going to be there indefinitely," he said. "The central government is not functioning effectively. One of the reasons, I think, is they feel they have as much time as they need, because our forces are there."
Notable deaths of 2014 [PHOTOS]