Russian President Vladimir Putin has ordered troops stationed near Ukraine's border to return to their home bases.
In a May 19 statement, the Kremlin said troops involved in "planned spring" exercises in the Rostov, Belgorod, and Bryansk regions have been ordered back to their barracks.
The Kremlin said that Putin specifically ordered Defense Minister Sergei Shoigu to pull back the troops in these three regions.
Putin's order appears to go further than his similar statement two weeks ago that Russian forces were being pulled back from the border to shooting ranges.
The Kremlin statement did not say how many troops would be pulled out from the three regions or specify how quick the withdrawal would be.
A NATO source said on May 19 the alliance had so far seen no sign of any movement among the 40,000 troops it says Russia has amassed there.
At the same time, the Kremlin urged Kyiv to end its operation in eastern Ukraine and withdraw its own troops from the region.
A Kremlin spokesman also said on May 19 that Putin will discuss Ukraine with UN chief Ban Ki-moon during a trip to China on May 20.
LIVE BLOG: Crisis In Ukraine
Meanwhile, Russian Foreign Minister Sergei Lavrov on May 19 said Moscow's relations with the European Union and NATO require "serious rethinking" due to the Ukraine crisis.
Lavrov also called on the Organization for Security and Cooperation in Europe to assist in the release of two Russian television journalists apparently detained in eastern Ukraine.
The two were reportedly detained by Ukrainian security forces near the flashpoint city of Kramatorsk.
He also said Slovakia's decision to allow for reverse natural-gas flows to Ukraine did not violate its agreements with Gazprom and the Russian government. He made the comments in Moscow after talks with visiting Slovak Foreign Minister Miroslav Lajcak.
Ukraine is facing a threat from Russia to cut off supplies because of a massive debt.
Lavrov's statements came ahead of a news conference in Brussels by Anders Fogh Rasmussen in which the NATO chief is expected to address the situation in Ukraine.
NATO has accused Moscow of not taking measures to de-escalate tensions in eastern Ukraine, where pro-Russian separatists have taken control of several towns and cities.
Rasmussen has called the crisis in Ukraine a "game-changer" for NATO and accused Russia of acting more like an adversary than a partner.
Meanwhile, Ukraine's Defense Ministry said one of its soldiers was killed when pro-Russian rebels shelled a military checkpoint near the rebel flashpoint of Slovyansk on May 19.
Three other soldiers were injured in the predawn attack.
The ministry said in a statement that the attack was launched from inside a kindergarten and accused the rebels of attempting "to provoke the servicemen into trying to destroy the kindergarten."
Ukraine's military launched an offensive against pro-Russian insurgents in mid-April but has failed to oust them from their strongholds in more than a dozen towns and cities.
WATCH: Crimean Tatars held a rally in Simferopol on March 18 to mark the 70th anniversary of their mass deportation from the Crimean peninsula ordered by Soviet leader Josef Stalin. (RFE/RL's Ukrainian Service)
On May 18, Tatars in Crimea commemorated the 70th anniversary since their deportation by Stalin.
On the outskirts of Crimea's capital, Simferopol, at least 10,000 people participated in a rally, carrying placards calling for "self-determination." There was a heavy police presence in Simferopol, with two military helicopters flying low over the rally.
The press service of the Mejlis, the Crimean Tatars' main representative body, said a resolution was adopted calling for "territorial autonomy" for the community, Tatar representatives in the Crimean government, and "an end to discrimination against and the repression of the Tatars of Crimea."
Several hundred people also marched in Ukraine's capital, Kyiv.
Tens of thousands usually gather for a rally in Simferopol marking the day on May 18, 1944, when Soviet authorities began deporting Crimean Tatars to Central Asia. Many of the 200,000 deportees died on their way into exile.
But the Mejlis announced on May 17 that "no mass rallies will take place in the center of Simferopol" on May 18 and called instead for Tatars to gather at religious centers and other locations.
The move came a day after authorities in Crimea, annexed by Russia in March, banned all public gatherings until June 6.
With reporting by Interfax, Reuters, AP, AFP, and Interfax