The United States might take military action to stop Iran's alleged involvement in Iraq War by training and equipping extremists who are killing U.S. troops, a U.S. senator said Sunday.

"I think we've got to be prepared to take aggressive military action against the Iranians to stop them from killing Americans in Iraq," Sen. Joseph Lieberman said on CBS' "Face the Nation."

"And to me, that would include a strike into -- over the border into Iran, where we have good evidence that they have a base at which they are training these people coming back into Iraq to kill our soldiers," he said.

The United States has long branded Iran as one of the "state sponsors of terrorism," and accuses Tehran of fueling the violence in Iraq, a charge Tehran dismisses. Iran blames the U.S. occupying forces for the bloodshed in Iraq.