A statement by the US Navy said the crew of the EP-3 reported turbulence following the first interaction, and vibrations from the second.
The Su-27 then made an additional pass where it got in front of the Navy plane and turned on its afterburners, or ignited the gasses coming off the jet engines for extra thrust.
Whether the USA military labels an air encounter is unsafe or unprofessional has less to do with the distances between aircraft and more with the behavior of the pilots intercepting the aircraft.
There was no communication between the two planes and the encounter lasted about 25 minutes, Spokesperson Eric Pahon told reporters at the Pentagon.
A Twitter account for the Russian Embassy in the United States posted a brief statement about the encounter on Monday, saying the fighter jet "followed all necessary safety procedures".
The Russian Ministry of Defense denied the Navy's claims that the Su-27 intercepted the EP-3 in an unsafe manner.
The incident took place Monday morning when the Russian military detected an unknown aircraft around 10 a.m. Moscow time (0700GMT), Russia's Defense Ministry said in a statement.
The US Navy also noted that the jet's actions caused turbulence and vibrations for the spy plane's crew.
This is not an isolated incident.
"While the Russian military is within its right to exercise within worldwide airspace, this interaction was irresponsible", the Navy said in a statement.
The Black Sea borders Ukraine, Russian-occupied Crimea and Russia in addition to Romania, Bulgaria, Turkey and Georgia.
"There's just absolutely no reason for this type of behavior", said Pahon, who noted that the American aircraft was flying a routine mission in global airspace "and the Russian aircraft kind of came out of nowhere and did not one, but two passes close to our aircraft".