Gen. Ray Odierno's comments on ABC's "This Week" came just weeks before the impending Sept. 1 deadline for the end of U.S. combat operations,
"For the last 20 months, we've been slowly and deliberately turning over more and more responsibility to (Iraqi forces) and they have stepped up," Odierno said.
The Iraqi forces are conducting broad security operations across the country, with U.S. help, he said, adding, "We do believe they are ready to assume full operations in Iraq."
The general said he expected "significant steps" toward formation of an Iraqi government by Sept. 1. "But," he added, "our numbers are not linked to that formation of the government."
Asked about increasing violence in recent days, Odierno said: "We have ups and downs here. As I step back, having been here since the dark days of 2006 and '07 to where we are today, what I see is a broad change in the security environment here in Iraq."
He stressed 50,000 U.S. troops will remain in Iraq in support roles when combat operations end.