WASHINGTON (CNN) -- Sen. Joe Lieberman, D-Connecticut, told CNN Thursday he thinks the president's changed policy in Iraq has successfully decreased the violence in Baghdad and increased the confidence of U.S. forces there.

"Our soldiers told [Ret. Gen. Jack Keane] they feel more confident than ever as they go on patrol in Baghdad in the neighborhoods we've settled into with their Iraqi colleagues," Lieberman told CNN's Wolf Blitzer. "The Iraqi people are coming out and protecting them because they have chased out the fanatics on both sides, those who were carrying out sectarian killings." (Watch video: CNN's Wolf Blitzer interviews Sen. Lieberman)

"The American soldier is more confident walking the streets of Baghdad today and that's a very important change," he added.

Regarding a wave of shooting deaths earlier this week in Tal Afar, a province near the Syrian border with a significant Sunni and Shiite population, Lieberman said such massacres are all the more reason the U.S. should not withdraw from the country prematurely.

"I look at it and say, do we want to turn Iraq, the Middle East and our future over to fanatics like that if we have a chance to stop them?," he said. "But this is war and we are fighting a brutal, inhumane, evil enemy. And so yes, they will strike at Mosul and Tal Afar as they have but that cannot lead us to throw in the towel and walk away."

-- CNN Ticker Producer Alexander Mooney