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.
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.
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.
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.
The deployment comes as a “humanitarian pause” in attacks on rebel-held eastern Aleppo in Syria begins.
The temporary truce is part of a plan to allow civilians and fighters to leave, and Russian and Syrian air strikes have been halted since Tuesday.
But International Development Secretary Priti Patel said the truce was “woefully inadequate”, adding: “What is needed is a return to a full and lasting cessation of hostilities, including safe humanitarian access, across the whole country as well as in Aleppo.”
The Russian task force will strengthen Russia’s naval presence off the Syrian coast.
It already has about 10 ships there, which have fired cruise missiles during Russia’s bombardment of anti-government rebels in Syria.
A Nato official said: “There are plans in place for Nato navies to monitor the Russian ships as they head for the Mediterranean.
“At the same time, the deployment of the carrier group to the eastern Mediterranean does not inspire confidence that Russia is working towards a political solution to the conflict in Syria.”
The Admiral Kuznetsov is the only carrier in the Russian navy. It can carry more than 50 aircraft and its weapons systems include Granit anti-ship cruise missiles.
The former Nato secretary general, Jaap de Hoop Scheffer, told BBC Radio 4’s World at One that Russian President Vladimir Putin was engaged in “risky posturing”, and the West needed to respond with tougher sanctions against Russia.
“I think we should have a strong reaction, and first and foremost, to show that the European Union has a consensus on its Russia policy,” he said.
“I’m not an admirer of Vladimir Putin, but he plays a weak hand rather well, because he knows that the European Union has no consensual Russia policy – so he can get away with it.”
Arriving at her first Brussels summit as UK prime minister, Theresa May said it was important to have a “united European stance” against “Russian aggression”, including “sickening atrocities” in Syria.