Herbert's visit comes at a time when violence is on the rise and the nation is more dangerous than a year ago, according to a report last week by the U.S. Special Inspector General for Iraq Reconstruction.
But Herbert said that military officials who briefed him, including Lt. Gen. Lloyd Austin, commanding general of the allied forces in Iraq, assured him the trend is going in the opposite direction ahead of a year-end U.S. troop draw-down.
"Not only the numbers are down, but the magnitude of the incidents are down," Herbert said. "I think the fact that there's a date [for the draw-down that has] been known probably spurs some kind of angst on the Iraqis' part. … The hope is the Iraqis will stand up. We're trying to help them here. The transition is going well in most areas, but not all."
In June, 15 American troops were killed, the deadliest month since April 2009, the inspector general reported.
Five U.S. soldiers were killed in July, including U.S. Army Cpl. Raphael Arruda, who emigrated from Brazil to Ogden and was serving in the Kunar province when his truck was struck by a roadside explosive.
Arruda, who was 21 years old when he was killed, was granted his U.S. citizenship posthumously.
Herbert attended Arruda's funeral on Saturday, before leaving on his trip.
"We should never forget and I think we won't forget," Herbert said. "Too often we take for granted the great example that America is for the rest of the world."
Herbert is traveling with Kentucky Gov. Steve Beshear, Nevada Gov. Brian Sandoval and Tennessee Gov. Bill Haslam. The expense of the trip, aside from the travel to and from Washington, D.C., is paid for by the Defense Department.
Herbert said that, after his briefing with Austin and his senior leadership, he came away concerned about Iran supplying Iraqi insurgents and fomenting violence, but he has confidence in the American leaders.
"I can tell you we're in great hands," Herbert said. "If us politicians don't screw it up, everything will be OK."