WASHINGTON — The United States on Tuesday moved to head off preparations for a suspected Russian military buildup in Syria as Bulgaria agreed to an appeal from the Obama administration to shut its airspace to Russian transport planes. The planes’ destination was the Syrian port city of Latakia.

The administration has also asked Greece to close its airspace to the Russian flights, Greek and American officials said, but Greece has not publicly responded to the request.

The apparent Russian military preparations and the Obama administration’s attempt to block them have escalated long-running tensions between the White House and the Kremlin. Although the United States and Russia agree that the Islamic State is a threat, the new dispute shows that they remain far apart on how best to combat the militant group and on the political future of President Bashar al-Assad of Syria — divisions that are likely to be on display when President Obama and President Vladimir V. Putin speak to the United Nations General Assembly this month.

The administration’s concerns were fueled last week by intelligence reports indicating that Russia appeared to be making preparations to deploy advisers and military personnel to an airfield south of Latakia and might also bring in aircraft and fly airstrikes from there. Those preparations included the delivery of prefabricated housing for as many as 1,000 personnel and a portable air traffic control station to the airfield.