The NTSB said the pilot of the Russian plane - a Transaero Boeing 737 - descended 200 to 300 feet to avoid Delta Flight 485.
The planes were on the same altitude - 33,000 feet over open ocean - and were "60 seconds apart from occupying the same airspace," said NTSB spokesman Peter Knudson.
Knudson said the agency doesn't have enough information yet to know if the planes would have collided had evasive maneuvers not been taken, or if they would have narrowly missed each other.
The two planes were about 180 miles north of San Juan when the near-collision occurred at about 6:30 p.m. EDT. The Delta aircraft was headed from New York's Kennedy International Airport to Port of Spain, Trinidad.
"This was every bit the classic near miss," said Doug Church, a spokesman for the National Air Traffic Controllers Association.
Church said controllers in the Federal Aviation Administration's air traffic control center in San Juan told him the airliners were on intersecting flight paths at the time of the incident.
The NTSB said there were no injuries.