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.
They say the incident happened in international airspace over the Baltic when Sergei Shoigu was flying to the Russian enclave of Kaliningrad.
Nato says it tracked three Russian jets as they did not identify themselves. It says the Nato jet was not chased away.
Dozens of similar incidents have been reported in the past few years.
Nato and Russia have blamed each other for aggressive intercepts in the strategically important region.
The US said a Russian jet had flown within 5ft (1.5m) of a US spy plane earlier this week. 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.
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.
A Nato official later said in a statement 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.”
The official added that the Nato jet had not been chased away by the Russian aircraft.
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.
Nato has beefed up its military presence in Poland, Estonia, Latvia and Lithuania, in the wake of Russia’s seizure and annexation Ukraine’s Crimea peninsula in 2014.
The latest incidents involving Nato and Russian planes come amid renewed tensions between Washington and Moscow, sparked by the US downing of a Syrian jet after it targeted American-allied rebels last week.
In response, Russia, an ally of the Syrian government, warned that US jets flying in Syria west of the Euphrates River would be treated as targets.
On Tuesday, the US military shot down an armed Iranian-made drone in Syria.
Inching towards a clash? Jonathan Marcus, BBC defence and diplomatic correspondent
What happened on Monday is only the latest incident in a continuing pattern where Russian and Nato aircraft have come into close proximity.
The two sides’ narratives are very different but independent studies have tended to support Nato’s case that more aggressive Russian behaviour is in large part to blame – this a response to Nato’s stepped up military deployments in central Europe in the wake of Russia’s seizure and annexation of Crimea.
These tensions risk accident and injury but are very different to the situation in Syrian airspace where the US, its coalition allies and Russian and Syrian warplanes are all engaged in combat sorties.
Unlike in Europe, there is a direct link between Russian and US commanders to avoid dangerous incidents – and although Russia is saying that this has been suspended in the wake of the US shooting down of a Syrian jet – the US side insists that the channel remains open.