A Nato fighter jet has approached a Russian plane carrying the defence minister but was chased away by a Russian escort jet, Russian media say, according to BBC.
They say the incident happened in international airspace over the Baltic when Sergei Shoigu was flying to the Russian enclave of Kaliningrad.
Nato later said it had tracked Russian planes but they did not identify themselves.
The US earlier said a Russian jet flew within 5ft (1.5m) of a US spy plane.
American officials blamed Russia for the “unsafe” encounter on Monday – again over the Baltic.
But Moscow responded by saying that the reconnaissance plane had made a “provocative” move.
Dozens of similar incidents have been reported in the past few years, with Nato and Russia blaming each other for aggressive intercepts in the strategically important region.
Nato’s ‘anti-Russian course’
Nato’s F-16 fighter jet flew close to Mr Shoigu’s plane on Wednesday, according to Russian news agencies, who had their reporters on board the ministerial flight.
They said that a Russian Su-27 fighter jet then intervened, demonstrating to a Nato pilot that it was armed by dipping its wings.
The Nato jet then flew off, according to footage that was aired later.
Nato spokesman Matthias Eichenlau later said that the alliance “can confirm that three Russian aircraft, including two fighters, were tracked over the Baltic Sea earlier today (Wednesday)”.
“As the aircraft did not identify themselves or respond to air traffic control, Nato fighter jets scrambled to identify them, according to standard procedures. Nato has no information as to who was on board. We assess the Russian pilots’ behaviour as safe and professional.”
Kaliningrad, Mr Shoigu’s destination, is a highly militarised Russian enclave on the Baltic.
At a meeting with local military commanders later on Wednesday, the minister accused Nato of intensifying its military activities near Russia’s western borders.
Mr Shoigu pointed to recent exercises by the military alliance, which involved 10,000 troops, 70 vessels and the same number of warplanes.
He added that the drills illustrated the West’s reluctance to give up its anti-Russian course.