The Iraqis responded that they would look into the matter, said an American official who declined to be identified because he was talking about diplomatic communications. But more than a week later, the Iraqis had yet to take action, Censor.NET reports citing The New York Times.
A spokesman for the Iraqi prime minister declined to comment on Sunday, asserting that he had no information about the Russian flights or the United States' concerns about them.
Russia is using an air corridor over Iraq and Iran to fly military equipment and personnel to a new air hub in Syria, openly defying American efforts to block the shipments and significantly increasing tensions with Washington.
American officials disclosed Sunday that at least seven giant Russian Condor transport planes had taken off from a base in southern Russia during the past week to ferry equipment to Syria, all passing through Iranian and Iraqi airspace.
Their destination was an airfield south of Latakia, Syria, which could become the most significant new Russian military foothold in the Middle East in decades, American officials said.
The Obama administration initially hoped it had hampered the Russian effort to move military equipment and personnel into Syria when Bulgaria, a NATO member, announced it would close its airspace to the flights. But Russia quickly began channeling its flights over Iraq and Iran, which Russia's foreign minister, Sergey V. Lavrov, said on Sunday would continue despite American objections.
With few aircraft, Iraq's ability to defend its airspace is extremely limited. But it could tell the Russians that they do not have the clearance to fly through Iraqi airspace and ask for American help in detecting and discouraging Russian flights.
A Russian Embassy official in Tehran told Russian news agencies on Wednesday that Iran had approved Russia's use of Iranian airspace to fly to Syria, but the official insisted the cargo was merely humanitarian aid.
According to American intelligence, about 200 Russian marines and six Russian howitzers now guard the air base south of Latakia. More prefabricated buildings have been delivered, increasing the housing capacity to 1,500 people. Dozens of Russian vehicles have been observed at the base, including about a dozen advanced infantry fighting vehicles.
American intelligence has not detected Russian fighter jets. But some American officials said Russian SU-25 and MiG-31 attack planes might arrive in the next phase of the buildup. They could be sent in crates and assembled in Syria or be flown to the base, officials said.
The Russian move could serve multiple purposes, according to analysts. In addition to strengthening Mr. Assad and buttressing the Kremlin's plan to create a new anti-ISIL coalition that includes Iran and the Syrian government, it positions Russia to have major influence in Syria's future and draws attention away from Russia's intervention in Ukraine.
"The Russians have done a masterful job of changing the subject on the eve of Vladimir Putin's arrival in New York for the 70th commemoration of the U.N. General Assembly," said Andrew S. Weiss, vice president for studies at the Carnegie Endowment for International Peace. He is a former Russia expert for the National Security Council, the State Department and the Pentagon.
"Instead of accepting a brushoff from the White House about Putin's desire for a meeting with Obama, the Russians are trying to argue that you have to talk to us about Syria," Mr. Weiss added. "I don't believe Western governments are prepared to do very much to slow down or block the risky course the Russians are going on."