The newspaper said the attack appeared to be part of a series of covert operations that have made officials in the US uncomfortable.
The Baltic Sea has witnessed in recent months several interceptions by Russian, US and NATO aircraft.
Russia has presented a lengthy document that it claims disproves allegations of Russian interference in the 2016 US presidential elections.
The US aircraft involved in the incident included F-16 and F-22 fighter jets, KC-135 stratotankers and E-3 AWACS, according to the statement.
Russia would prefer the shorter route over Turkey to get to the Hmeimim airbase in Syria, where Moscow has military assets.
Gershkovich was arrested in March and accused of espionage, which he and his newspaper, the Wall Street Journal, deny.
White House national security spokesman John Kirby called the claims "obviously ludicrous."
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