The NTSB said the pilot of the Russian plane - a Transaero Boeing 747 - descended 200 feet to 300 feet to avoid Delta Flight 485.
The planes were at 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 Boeing 737
- with 152 passengers aboard - was headed from New York's Kennedy International Airport to Port of Spain, Trinidad.
The NTSB said there were no injuries.
"This was every bit the classic near miss," said Doug Church, a spokesman for the National Air Traffic Controllers Association.
The Delta pilot told air traffic controllers that the incident was "extremely close" and that he also took evasive maneuvers, said Victor Santore, a vice president of the controllers union. NTSB's Knudson said he could not confirm the controllers' account.