The announcements are the latest reported drawdowns of a Russian military contingent estimated by the West to be more than 100,000 troops, which Washington had said could be preparing to invade.

"Units of the southern military district that ended tactical exercises at training grounds on the Crimean peninsula are returning by rail to their permanent bases," the defence ministry said in a statement carried by Russian news agencies.

State-run television showed columns of military hardware crossing a recently constructed bridge connecting the peninsula to the Russian mainland.

Separately, the defence ministry said "tank units of the western military district began returning to their permanent bases" after participating in drills.

It did not specify where those forces had been deployed but said they would be transported by rail some 1,000 kilometres (620 miles) to their garrisons.

Defence ministry spokesman Igor Konashenkov later said the troops of the southern military district had returned to their garrisons in the North Caucasus republics of Chechnya and Dagestan following drills in Crimea.

Konashenkov added that soldiers carrying out exercises in the Kursk and Bryansk regions, both bordering Ukraine, returned to home bases near Nizhny Novgorod, some 300 kilometres east of Moscow.

NATO, the United States and European leaders have denied there is any meaningful pullback of Russian troops and Ukraine's President Volodymyr Zelensky said Moscow's military personnel were actually rotating.

Russia took control of the Crimean peninsula in 2014 and threw its weight behind pro-Moscow separatists in fighting that broke out that year and has claimed more than 14,000 lives.