"Units of the Southern Military District, having completed their participation in tactical exercises, are moving to their permanent deployment points," Moscow's defence ministry said in a statement.

State television showed images of military units crossing a bridge linking the Russia-controlled peninsula to the mainland.

The statement said tanks, infantry vehicles and artillery were leaving Crimea by rail.

It comes a day after Moscow said it was pulling back some of the troops deployed on its neighbour's borders.

But Western leaders remain concerned that Russia could still launch an attack on Ukraine, with US President Joe Biden warning on Tuesday that an attack by Moscow remained "very much a possibility".

Biden said that despite Russian claims earlier in the day, Washington and its allies had yet to verify the withdrawal of any of the tens of thousands of troops he says Moscow has now mustered along Ukraine's border.