The Russian defence ministry said it has sent a MiG-31 fighter jet after the approach of two US B-1B bombers towards its border over the Barents Sea.
The American planes turned away from the border - at the north east of the country - after the approach of the MiG-31, the ministry said.
The US has not commented on the incident.
Meanwhile, suspects in the Crocus City Hall shooting were brought to the investigation committee's headquarters in Moscow, Russian state news agency RIA reported on Sunday.
Authorities put the number of dead in Friday's mass shooting up to 137, with three children among the dead in what is thought to be a terrorist attack.
In the aftermath, 11 were arrested - including four who were said to be the shooters.
Militant Islamist group Islamic State claimed responsibility for Friday's events but there were indications that Russia was pursuing a Ukrainian link despite emphatic denials from Ukrainian officials that Kyiv had anything to do with it.
British chancellor Jeremy Hunt said on Sunday that despite his sympathies over the tragedy he cannot believe all of the “propaganda” the Kremlin has put forward.
He said: “We have very little confidence in anything the Russian government says.
“[Russia is] creating a smokescreen of propaganda to defend an utterly evil invasion of Ukraine.
“That doesn’t mean it is not a tragedy when innocent people die.
“[I take] everything the Russian government says with a pinch of salt after what we have seen.”
Earlier on Sunday, a missile strike was reported on Ukraine cities Kyiv and Lviv which followed on from a strike on a hydroelectric plant in Dnipro.
Additional reporting by Reuters.
