WASHINGTON (CNN) -- Sen. Gordon Smith, the Oregon Republican who said he no longer supports U.S. involvement in Iraq during an impassioned speech on the Senate floor last week, told CNN Monday he reached his conclusion because Iraq has descended into a "civil war" that U.S. troops will not be able to stop.

"You know, this is a fight, when you get right down to the root of it, between Sunnis and Shias that goes back a millennia of time over who is the rightful successor to the Prophet Mohammed," Smith told Wolf Blitzer in an interview set to air on "The Situation Room." "That is not our fault. That is not our fight, and that's not something we can fix."

Smith said he felt compelled to speak out because "sacrifices are being made in pursuit of a policy that cannot succeed."

"We need to admit it and readjust in a way that the American people and our soldiers find worth the sacrifice."

Watch Wolf's entire interview with Smith in the 5 p.m. ET hour of today's "The Situation Room."