HMS Sutherland will keep a "vigilant watch" on Steregushchiy-class corvettes Soobrazitelny and Boiky as they sail close to UK waters.
A Russian support tanker and ocean-going tug is also travelling with them.
It comes amid rising tensions between London and Moscow over Russia's support for Syrian President Bashar al Assad, who is accused of fatally gassing his own people.
The ships were located by the Plymouth-based Type 23 frigate as they sailed through the North Sea towards the Dover Straits on Friday morning.
Defence Secretary Sir Michael Fallon said: "HMS Sutherland is carefully marking these Russian ships as they pass close to UK waters.
"The Royal Navy maintains a vigilant watch and is always ready to keep Britain safe."
The frigate's Commander Andrew Canale said: "As one of the Royal Navy's high-readiness units, HMS Sutherland is required to escort warships that approach the UK and this task is considered routine business for us.
"It is vitally important the Royal Navy demonstrates its presence and commitment to the integrity of UK territorial waters as we work around the clock to secure the seas of our island nation."