President Vladimir Putin says he ordered the troop withdrawal to help create "favorable conditions" for the May 25 Ukrainian presidential election.
Ukrainian officials say Russian troops have moved at least 10 kilometers away from Ukraine’s border.
But Kyiv could not confirm Moscow's claims of a full withdrawal.
NATO Secretary-General Anders Fogh Rasmussen said on a visit to Sarajevo on May 21 that there was no "firm evidence" of a pullback.
He added that this is the third time Putin has announced a troop withdrawal from the Ukrainian border.
U.S. Army Secretary John McHugh said that the U.S. sees some Russian troop movements but no large-scale withdrawal. (Reuters, AP, ITAR-TASS)
Biden also is encouraging energy deals that lessen European dependence on Russian natural gas -– saying on May 21 that "we need to ensure Russia can no longer continue to use its resources as a weapon against anyone in the region."
In Nicosia, Biden was expected on May 22 to stress the need to enforce European Union sanctions against Russia over its annexation of Crimea and its role in the Ukrainian crisis.
The issue is sensitive in Nicosia because Russians have billions of dollars deposited in Cypriot banks.
He also was expected to urge Cypriot officials from the north and south to join a fresh round of talks aimed at reunifying the divided island.
As a key business partner of Russia in the EU, Cyprus opposes further sanctions that could hurt its economy, which is still struggling after being bailed out in 2013 by the International Monetary Fund and the EU.
In his energy talks with Cypriot leaders, Biden is expected to encourage the development of recently discovered offshore natural gas deposits in the eastern Mediterranean between Cyprus and Israel.
U.S. officials say the discovery of hydrocarbons in Cypriot waters could position Cyprus as an energy and economic leader in the region.
Cyprus already has licensed the U.S. firm Nobel to drill for natural gas after discoveries off its southern coast.
It also has licensed Italy’s ENI and France’s Total to search for gas.
Cyprus is the only EU state that is neither in NATO nor NATO’s Partnership for Peace program.
But Cypriot President Nicos Anastasiades has realigned Cyprus's policies more in favor of Washington and Europe, in contrast to his predecessor.
Cyprus has been divided along ethnic lines since 1974 when Turkey invaded the north, which is recognized only by Turkey as a separate entity.
Biden arrived in Nicosia on May 21 after a visit to Romania where he warned Moscow against undermining Ukraine’s May 25 presidential election.
Speaking alongside Romanian President Traian Basecu in Bucharest on May 21, Biden said NATO allies must remain “resolute” in enforcing sanctions against Moscow.
He also said the development of a secure, diverse, and interconnected energy market would be the next step of European integration -- and a way to diminish Europe’s dependence on Russian gas. (Reuters, AP, and AFP)
Rotting garbage is piling up in the hallways of the government office building seized by separatists in eastern Ukraine. Telephones ripped from the walls are piled atop broken furniture and mounds of old files. The stench of sweat and stale cigarettes is everywhere. The guards, slouching men with pistols shoved in their pockets or flapping loosely in holsters, look increasingly bored.
Mr Khodorkovsky told the BBC that Ukraine had entered a "slow burn civil war" but he said he did not believe Russian President Vladimir Putin was planning to invade eastern Ukraine.
Mr Putin had "lost control" of events in Russia's neighbour, Mr Khodorkovsky said, citing the Kremlin's recent inability to stop a referendum by pro-Russian separatists in Donetsk and Luhansk.
But he said Europe's reaction to events in Ukraine threatened to exacerbate renewed Russian nationalism, stirred up by the Russian president's annexing of Crimea.
Mr Khodorkovsky argues that EU leaders should avoid further sanctions on Moscow and concentrate their efforts on encouraging political reform in Kiev.