The encounter occurred on Tuesday and was described by the US Navy as "safe and professional."
"Distance is only one of many variables considered when defining what is safe and professional," Pentagon spokesman Navy Capt. Jeff Davis said. "For aviation interactions, distance, speed, altitude, rate of closure, visibility and other factors impact whether an event is characterized as safe or unsafe, professional or not professional."
A US defense official told CNN that the Russian aircraft was armed with six air-to-air missiles and that the pilot took photos of the US plane during the encounter.
According to the Russian Ministry of Defense, "The Russian fighter carried out a 'greeting' maneuver. After that, the US surveillance aircraft changed his flying course away from the Russian border."
The aircraft were operating 65 miles south of the Sea of Azov, which separates Russia and Russian-occupied Crimea.
"The US Navy does, on a normal and routine basis, operate ships and aircraft in the Black Sea consistent with international law," Kunze said.
The Russian government statement described the Russian jet as an Su-30 while US officials referred to it as a Su-27.
Russia has conducted several flights off the US coast in recent months.
Last week, two Russian bombers, flanked by a pair of fighter jets, were intercepted by stealth US F-22 aircraft off the coast of Alaska.
And during a stretch in April, Russian military aircraft were spotted flying off the coast of Alaska four times in as many days.
The fact that Tuesday's encounter took place near Crimea adds an additional level of significance, as the two countries' opposing views on the conflict in Ukraine have become a hot-button issue between the sides.
The Trump administration has said it opposes Russia keeping Crimea. White House press secretary Sean Spicer said earlier this year that he expected Moscow to withdraw from the region, which it has occupied since 2014.
The US, meanwhile, has positioned military assets across Europe in an effort to reassure its European and NATO allies in the wake of Russia's movements in Ukraine.