Theresa May has condemned Vladimir Putin's aggression in Syria as Royal Navy vessels monitored Russian warships thought to be heading to reinforce the attack on the besieged city Aleppo.
The Prime Minister accused Moscow of being behind "sickening atrocities" in support of Bashar Assad's regime.
Her comments came as a Russian taskforce, including the aircraft carrier Admiral Kuznetsov, was being shadowed by the Royal Navy as it headed towards the eastern Mediterranean.
Type 45 destroyer HMS Duncan sailed from Portsmouth on Tuesday to "man-mark" the Kuznetsov group, which is heading south through the North Sea and English Channel.
The Type 23 frigate HMS Richmond escorted the group from the Norwegian Sea as it steamed south.
A Ministry of Defence spokesman said: "When these ships near our waters we will man-mark them every step of the way. We will be watching as part of our steadfast commitment to keep Britain safe."
Syrian forces, backed by Russian air power, have agreed a temporary humanitarian truce in Aleppo but Mrs May urged European leaders to take a firm line against Moscow.
Arriving at her first Brussels summit as PM, Mrs May called for a "robust and united European stance in the face of Russian aggression".
She said: "It is vital that we work together to continue to put pressure on Russia to stop these appalling atrocities, these sickening atrocities, in Syria."
Nato said the prospect of Russia's only aircraft carrier heading to the region does not "inspire confidence" that Moscow is seeking a political solution to the Syrian crisis.
A Nato official said: "Russia has the right to operate in international waters. 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."
Russian defence minister Sergei Shoigu said in September that the Admiral Kuznetsov-led Northern Fleet would be joining a taskforce in the Mediterranean.
According to the Russian news agency Tass, he told a defence board meeting that the plan was to bolster the Mediterranean fleet's "combat capabilities".
A statement from the fleet to the agency on October 15 said the group also consisted of the Pyotr Velikiy battlecruiser, the Severomorsk anti-submarine ship, the Vice-Admiral Kulakov destroyer and other support vessels.
The statement added: "Special focus will be made on safeguarding security of maritime traffic and other types of maritime economic activity of Russia and also on responding to the new kinds of modern threats such as piracy and international terrorism."
Mr Putin has held out the prospect of extending the pause in the Aleppo bombing campaign following a meeting with French president Francois Hollande and German chancellor Angela Merkel.
The Russian president said: "We informed them of our intention to continue, as much as possible, considering the situation on Syrian territory, a pause in the air strikes. We are ready to do this for as long as there are no clashes with rebel formations entrenched in Aleppo."
Defence Secretary Sir Michael Fallon said the Russian naval deployment was aimed at "testing" British capabilities.
"The Russian fleet that is now sailing from the North, presumably down into the Mediterranean, is clearly designed to test the alliance. It's being marked every step of the way by the Royal Navy and ships and planes of other Nato members as well.
"It's clearly designed ... to test our response, and any weaknesses in the alliance, and we must make sure we respond in due measure. That fleet will be marked, shadowed every inch of the way."