The announcement came as President Vladimir Putin invited Ukrainian leader Volodymyr Zelensky for talks in Moscow following weeks of renewed fighting in the east of Ukraine between government troops and pro-Moscow separatists.

But the Russian leader appeared to shoot down Zelensky's proposal to meet in war-torn eastern Ukraine, saying talks over the years-long conflict should be conducted directly with separatists.

Earlier in the day Russian Defence Minister Sergei Shoigu oversaw massive drills in Moscow-annexed Crimea and said soldiers would begin returning to their permanent bases on Friday.

"The troops demonstrated their ability to ensure the reliable protection of our country," he said after flying over the Opuk firing range in a helicopter.

"I've made a decision to wind down the checks in the Southern and Western military districts," he said, adding the troop pullback should be completed by May 1.

The West has repeatedly called on Putin to pull back troops, and on Thursday the United States said it would wait for Moscow to follow up on its announcement of an end to the military drills near Ukraine.

"We've heard the words. I think what we'll be looking for is action," State Department spokesman Ned Price told reporters.

Shoigu, who arrived in Crimea earlier in the day to oversee military drills, said Moscow was closely watching NATO movements and would remain vigilant.

Shoigu and the army's general chief of staff Valery Gerasimov, both armed with binoculars, oversaw the drills from a viewing platform as helicopters flew overhead.

The ministry released dramatic footage of the land and sea manoeuvres that showed troops practising amphibious landings, jets streaking through the sky and infantry vehicles traversing green fields.

- 'NATO remains vigilant' -

Both NATO and Ukraine's Zelensky welcomed Russia's announcement, with the Ukrainian leader saying on Twitter that "the reduction of troops on our border proportionally reduces tension".

"Any steps towards de-escalation by Russia would be important and well overdue," said a NATO official.

"NATO remains vigilant and we will continue to closely monitor Russia's unjustified military build-up in and around Ukraine."

In Moscow, Putin said Zelensky was welcome in Moscow "any time".

"If President Zelensky wants to start repairing relations, then we of course welcome it," he said.

But the Russian leader also said that if Zelensky hoped to resolve problems stemming from fighting in eastern Ukraine, then he should first meet with leaders of the breakaway regions in Donetsk and Lugansk.

Zelensky had this week invited Putin to hold talks in Ukraine's east, saying millions of lives were at stake.

- Putin 'playing games' -

Timothy Ash, senior emerging markets strategist at London-based Bluebay Asset Management, said Putin was "playing games" and it was hard for the Ukrainian leader to accept direct talks with separatists.

"Everyone knows this is a state vs state conflict but Putin is trying to imply this is a civil war in Ukraine," Ash said.

Kiev said one more soldier had died of shrapnel wounds when "Russian armed forces" shelled Ukraine's positions on Thursday.

European security watchdog OSCE's monitoring mission in eastern Ukraine for its part sounded the alarm over "near-unprecedented restrictions and impediments to its ability to operate" and increased numbers of civilian casualties.

Some 30 Ukrainian soldiers have been killed since the start of the year, compared to 50 in all of 2020.

The West and Ukraine have accused Russia of sending troops and arms across the border but Moscow has denied the claim.

Russia's troop buildup on the Ukrainian border led to concern in Kiev and the West of a repeat of Russia's 2014 aggression, when Moscow annexed the Crimean peninsula from Ukraine.

The EU estimated this week the number of Russian troops along the Ukrainian border at more than 100,000.

Shoigu has described the movement of Russian troops as training exercises in response to "threatening" NATO actions.

On Thursday, he said Russia was closely watching NATO activity including the massive Defender Europe 2021 exercises from the Baltic to the Black Sea.

Moscow said some 10,000 Russian troops and over 40 warships and other vessels were participating in the Crimea exercises.

Russia also said last week it intends to close parts of the Black Sea to foreign military and other ships for six months beginning Saturday.

Kiev has been battling separatists in eastern Ukraine since 2014, with the conflict claiming more than 13,00 lives.