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Russian Foreign Minister Sergei Lavrov (left) and U.S. Secretary of State John Kerry chat before a bilateral meeting on Aug. 5, 2015. Reuters

The U.S. has requested that Greece deny Russia the use of its airspace for supply flights to Syria, a Greek official said on Monday, Reuters reported. The Greek foreign ministry said the request is currently being examined.

Russia has a naval maintenance facility in the Syrian port of Tartous and has regularly sent flights to bring back Russian nationals from Latakia, Syria's chief Mediterranean port city. Russia is seeking to run the flights until Sept. 24, according to Russian newswire RIA Novosti.

Moscow would not give an official reaction until there was a decision from Athens, said Kremlin spokesman Dmitry Peskov, Reuters reported.

The U.S. has become increasingly concerned over an apparent Russian military buildup in Syria. Kremlin officials dismissed allegations that the country will undergo a major military deployment to Syria during a telephone call with U.S. Secretary of State John Kerry, CNN reported. Kerry warned that a major military deployment could “further escalate the issue.”

Previously, unnamed Western diplomats reportedly said a Russian expeditionary force is already in Syria, preparing for the arrival of fighter jets and attack helicopters for “strikes against ISIS targets in Syria,” CNN reported. Kerry spoke with Russian Prime Minister Sergei Lavrov regarding the allegations, and he warned that an increased Russian military presence in Syria “could further escalate the conflict, lead to greater loss of innocent lives, increase refugee flows and risk confrontation,” according to a statement from the U.S. State Department.

Lavrov told Kerry that it was premature to talk about military operations in Syria, according to a Russian foreign ministry spokeswoman, Reuters reported. Lavrov did acknowledge that Russia has always supplied military equipment to Syria. Russia has continually backed President Bashar al-Assad throughout the war, while rebels groups have received support from the United States, Saudi Arabia and Turkey.

If Assad is toppled, Russia’s influence in the region might dwindle as well, CNN reported. The Kremlin also has genuine security concerns regarding ISIS.