Hadley appeared Sunday on ABC News' "This Week with George Stephanopolous."
"We know that there are jihadists moving from Syria into Iraq," Hadley said. " ... We know also that Iran is supplying elements in Iraq that are attacking Iraqis and attacking our forces."
What the president "has made very clear is these are activities that are going on in Iraq that are unacceptable," he added. "They put our people at risk and (Bush) said very clearly that we will take action ... We will interdict their operations. We will disrupt their supply lines. We will disrupt these attacks."
Iranians supporting insurgents "have been picked up by coalition forces, and I think you're going to see more of that," Hadley said.
The national security adviser refused to say whether Bush had the authority to order troops into Iran. But Hadley made it clear that action against Iranians would only take place inside Iraq.
Also appearing on the program, Rep. John Murtha, D-Pa., chairman of the Defense Appropriations Subcommittee and an Iraq policy critic, said Democrats will do what they can to change the "direction of this war."
"The president does not have legal authority to go into Iran," Murtha added. " ... And he wouldn't have the capability of doing that even if he wanted to."
Notable deaths of 2014 [PHOTOS]