The American warship was conducting air operations about 70 nautical miles from the Russian enclave of Kaliningrad when the aircraft flew at an 'unsafe' speed close to the Destroyer.
Two close encounters occurred on Tuesday night in international waters, while another, at an acceptable distance, happened on Sunday.
'This is more aggressive than anything we've seen in some time,' the defense official said, on condition of anonymity.
While there are often encounters between US ships and foreign aircraft, this time officials and crew deemed the movements of the Russian jets unsafe, due to their speed and proximity to the ship.
The White House issued a statement condemning Russia for the latest in a series of 'concerning' clashes between the Russian and U.S. militaries.
'This incident is entirely inconsistent with the professional norms of militaries operating in proximity to each other in international waters and international airspace,' Press Secretary Josh Earnest said.
The incident came as NATO plans its biggest build-up in eastern Europe since the Cold War to counter what the alliance, and in particular the Baltic states and Poland, consider to be a more aggressive Russia.
The three Baltic states - Estonia, Lithuania and Latvia - which joined both NATO and the European Union in 2004, have asked NATO for a permanent presence of battalion-sized deployments of allied troops in each of their territories. A NATO battalion typically consists of 300 to 800 troops.
Moscow denies any intention to attack the Baltic states, which were part of the former Soviet Union.
USS Cook has spent much of the last two years in Europe, following its deployment to the Black Sea in 2014 after Russia's annexation of Crimea., Daily Mail Reports.
While it was stationed there, it was buzzed 12 times by two Russian Su-24s in a remarkably similar incident to the one on Tuesday.
'The Donald Cook is more than capable of defending itself against two Su-24s,' the Pentagon said at the time.
Tensions with Russia were further raised earlier this year when the U.S. announced plans to station six F-15 aircraft in Finland and artillery in Norway, with both nations sharing a border with Russia.
The U.S. already has fighter planes based in the UK, Germany, Italy, Portugal, Iceland and the Netherlands.
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