Sen. Lindsay Graham, R-S.C., spoke on CBS' "Face the Nation" following his tour of Iraq with Republican presidential hopeful Sen. John McCain of Arizona.
The war in Iraq "has turned a corner," Graham said.
"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 surge has worked on all fronts."
But Sen. Jack Reed, D-R.I., responded to Graham's assessment, noting that "the problem with Iraq is that every time you turn the corner, there is another corner," Voice of America relayed.
Speaking on CNN's "Late Edition," the Iraqi national security adviser said the status of U.S. forces in Iraq and any long-term assessments depended on "the preparedness of the Iraqi security forces."
The Bush administration said it would consider a further drawdown of troop levels in Iraq after Crocker and Petraeus brief Congress on the progress in Iraq on April 8 and 9.
The U.S. troop level is expected to go down to the pre-surge levels of 15 brigades by this summer. "And where we go from there is going to be something that the president will decide and make public to everybody in early April," White House spokeswoman Dana Perino said in a news briefing Monday of the two-hour video conference.