The Russian ship altered course after it established bridge-to-bridge radio communication with the USS Farragut, officials told CNN.
"While the Russian ship took action, the initial delay in complying with international rules while it was making an aggressive approach increased the risk of collision," according to the Fifth Fleet.
The incident marked the second near-collision between Russian and U.S. ships in the past few months.
American officials said in June that a Russian destroyer got within 100 feet of the USS Chancellorsville as the ships were traveling in the Philippine Sea. Russian military officials blamed the incident on a sudden change of course by the U.S. ship, NBC News reported.