Two British warships are shadowing an aircraft carrier and other Russian naval ships as they pass the UK on their way to Syria.
The carrier Admiral Kuznetsov and its task force are on a course to sail through the North Sea and English Channel.
A Ministry of Defence spokesman said the ships would be "man-marked every step of the way" while near UK waters.
However, Nato said Russia had the right to operate in international waters.
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It comes amid heightened tension between Russia and Nato.
"We will be watching as part of our steadfast commitment to keep Britain safe," Defence Secretary Michael Fallon said.
The Ministry of Defence said at about 13:00 BST that the Russian task force was "in the middle of the North Sea heading southwards" - at that stage it was understood to be about 100 miles (160km) off Edinburgh.
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Type 45 destroyer HMS Duncan sailed from Portsmouth on Tuesday to track the Kuznetsov group as it headed south from the Norwegian Sea, escorted by the Type 23 frigate HMS Richmond.
Analysis
By Jonathan Marcus, BBC defence and diplomatic correspondent
If, as anticipated, the Admiral Kuznetsov and its task force are heading for the eastern Mediterranean, this will be the first ever combat deployment for Russia's only aircraft carrier.
A Ministry of Defence spokesman says that the Russian flotilla - currently in the North Sea - could pass through the Strait of Dover as early as Thursday evening, though it could be significantly delayed if the carrier conducts flight operations or has to stop to refuel.
Two of the Russian vessels carry land attack cruise missiles and the carrier has an unknown number of aircraft on board.
These will enhance Russia's firepower off Syria but this is above all a demonstration of force projection; a signal from Moscow that it can deploy its military might when and where it chooses.
UK warships shadowing Russian naval task force - BBC News