A British defence source said: “The anxiety is because we don’t know what’s going to happen. It is an unpredictable situation.”
The Bloomberg news agency reported on Thursday that Washington has warned European allies Moscow could be weighing a potential invasion of Ukraine – almost eight years on from its successful annexation of Crimea.
Russia on Friday dismissed the claims as inflammatory.
“Such headlines do nothing more than pointlessly and groundlessly fuel tensions. Russia does not pose a threat to anyone,” Kremlin spokesman Dmitry Peskov said.
But denials have in the past been a tactic used by Moscow to mask the reality on the ground.
Back in 2014, Russia denied any involvement in the annexation of Crimea until after it had happened.
President Vladimir Putin has since supported separatists in eastern Ukraine in a rumbling conflict with the western-backed Ukrainian government.
Earlier this week, Antony Blinken, the top US diplomat, publicly expressed concern about what he described as “unusual Russian military activity” near Russia’s border with Ukraine.
The troop presence is also close to Russia’s border with Belarus, another flashpoint.
Mr Peskov said such concerns were wide of the mark.
“We have repeatedly said that the movement of our armed forces on our territory should not be a cause for concern,” he told reporters in a conference call.
Asked for a comment on the Russian troop movements, a NATO official said: “NATO is vigilant and routinely monitors Russian force movements. It’s important to ensure transparency and avoid any miscalculation.”
In simmering tensions between Russia and the West, the Russian defence ministry on Thursday claimed it had scrambled a fighter jet to intercept a British spy plane operating near Crimea.
A UK Ministry of Defence spokesperson said: “We do not recognise these claims. Wherever the RAF operates, it does so in full compliance with international laws and exercises its right to freedom of overflight.”
US Secretary of State Blinken made his remarks on Ukraine as he met with his Ukrainian counterpart, Dmytro Kuleba, in Washington on Wednesday.
“We’re concerned by reports of unusual Russian military activity near Ukraine,” Mr Blinken said.
“Any escalatory or aggressive actions would be of grave concern to the United States.”
Mr Blinken said the US did not know Russia’s intentions but said Moscow’s “playbook” has been in the past to invent provocations along its border to justify military intervention.
“We don’t have clarity into Moscow’s intentions, but we do know its playbook,” he said. “If there are any provocations that we’re seeing, they’re coming from Russia.”
Ukraine last week said Russia has kept tens of thousands of troops not far from the border after war games, as part of an attempt to exert pressure on its ex-Soviet neighbour.
The Ukrainian defence ministry said about 90,000 Russian troops are stationed not far from the border and in rebel-controlled areas in Ukraine’s east.
Russian officials said the troops were deployed for manoeuvres, casting them as part of measures to counter security threats posed by the deployment of NATO forces near Russian borders. Russia and the alliance also have blamed each other for conducting destabilizing military exercises near the borders.