Iraq is both reluctant and unable to stop the flights despite pressure from the United States, The New York Times reported.
The flights have allowed Iran to restock Syrian military forces despite efforts by opposition groups to close border crossings where Iranian trucks enter and leave, military experts said.
The United States has been wary about establishing a no-fly zone over Syria because of concern about being drawn into the Syrian conflict. Iraq has no air force and U.S. military craft were withdrawn when U.S. troops were pulled out.
The lack of action against the Iranian flights puts Iraq and the United States at cross purposes. The United States is leading an international effort to impose sanctions on the Bashar Assad regime. Maliki wants to maintain relations with Iran because the fall of Assad could strengthen the Iraqi leader's rivals in the region.
Iran is Syria's biggest ally.