USS Harry S. Truman has been pursued around the Med by a group of Russian frigates led by warship Yaroslav Mudry.
Video of the incident shows a Russian vessel in the distance shadowing the carrier and its destroyer escort.
Footage was shared by ITV as a team of news reporters visited the US warship.
The vessel is the US’s main weapon against ISIS as it launches strikes on their positions in Syria.
War tensions have flared however after the US, France and Britain launched airstrikes against Vladimir Putin’s pal Bashar al-Assad.