Vice President Joseph R. Biden Jr., who has played the lead role on Iraq policy for the Obama administration, discussed the Syrian crisis in a phone call with Mr. Maliki on Aug. 17. The White House has declined to disclose details, but an American official who would not speak on the record said that Mr. Biden had registered his concerns over the flights.

The Iranian flights present searching questions for the United States. The Obama administration has been reluctant to provide arms to the Syrian rebels or establish a no-fly zone over Syria for fear of being drawn deeper into the Syrian conflict. But the aid provided by Iran underscores the reality that Iran has no such hesitancy in providing military supplies and advisers to keep Mr. Assad’s government in power.

And Mr. Maliki’s tolerance of Iran’s use of Iraqi airspace suggests the limits of the Obama administration’s influence in Iraq, despite the American role in toppling Saddam Hussein and ushering in a new government. The American influence also appears limited despite its assertion that it is building a strategic partnership with the Iraqis.

Mr. Maliki has sought to maintain relations with Iran, while the United States has led the international effort to impose sanctions on the Tehran government. At the same time, the Iraqi prime minister appears to look at the potential fall of Mr. Assad as a development that might strengthen his Sunni Arab and Kurdish rivals in the region. Some states that are the most eager to see Mr. Assad go, like Saudi Arabia, Qatar and Turkey, have poor relations with Mr. Maliki and his Shiite-dominated government.

Iraq could take several steps to stop the flights, including insisting that cargo planes that depart from Iran en route to Syria land for inspection in Baghdad or declaring outright that Iraq’s airspace cannot be used for the flights.