Russia on Friday began withdrawing troops that had been running drills near the borders of Ukraine, the defence ministry said, following weeks of heightened tensions between Moscow and the West over the buildup.

"Military units and formations are currently marching to railway loading stations and airfields, and loading onto landing ships, railway platforms and military transport aircraft," the ministry said in a statement carried by Russian news agencies.

Defence Minister Sergei Shoigu announced the exercises were winding down on Thursday and that all Russian soldiers participating would be returned to permanent bases by the beginning of May.

His announcement was immediately welcomed by Ukrainian President Volodymyr Zelensky who cautioned that his military would remain "vigilant".

Zelensky and his allies in Western capitals have been concerned in recent weeks by an uptick in fighting between the Ukrainian army and pro-Moscow separatists in the east of his country, as well as by the buildup of troops participating in the drills.

Hours after the end to the exercises was announced, Russian President Vladimir Putin said Zelensky was welcome in Moscow anytime to discuss bilateral relations, but that Zelensky should discuss the surge in fighting with separatist leaders in Ukraine's breakaway republics.

Kiev has been battling pro-Russian separatists in the eastern Donetsk and Lugansk regions since 2014, following Moscow's annexation of the Crimean peninsula.

The conflict, which has claimed more than 13,000 lives, has seen at least 31 Ukrainian soldiers killed since the start of the year, compared to 50 in all of 2020.