Russian President Vladimir Putin has told German Chancellor Angela Merkel that he has ordered the withdrawal of some Russian troops from the border with Ukraine.
A Merkel spokesman said Mr. Putin ordered a "partial withdrawal" of troops from Ukraine's eastern border.
The United States estimates Russia has 40,000 troops along the border, while Kyiv says the number is closer to 100,000.
Russia's Defense Ministry said Monday that a motorized infantry battalion was withdrawing from the region.
The French News Agency Monday quoted a spokesman for the Ukrainian defense ministry's general staff as saying Russian forces have been "gradually withdrawing" from the border region in recent days -- adding that this could be linked either to a "a regular rotation" or to "the Russian-US negotiations."
The State Department said that if true, Washington would welcome the movement of troops away from the border -- and that the process should be accelerated.
Ms. Merkel's spokesman said she and President Putin also discussed "possible further steps to stabilize the situation" in Ukraine and in Transdniestria, a breakaway ethnic Russian enclave in Moldova.
The Kremlin, for its part, said in a statement Monday that Mr. Putin had emphasized in the phone conversation with Ms. Merkel the importance of "constitutional reform" in Ukraine aimed at "ensuring the legitimate interests of the residents of all Ukrainian regions."
Russia has said it has the right to protect Russian speakers in Ukraine, and used that as justification for taking over Crimea.
The Kremlin said Mr. Putin also stressed the need to take measures to end the "de facto blockade" of Transdniestria.
The telephone conversation came a day after U.S. Secretary of State John Kerry demanded Russia pull back thousands of its troops massed along the border with Ukraine.
Kerry told Russian Foreign Minister Sergei Lavrov in Paris Sunday that the troops were creating a "climate of fear" in Ukraine.
On Monday, Russian Prime Minister Dmitry Medvedev became the most senior Russian to visit Crimea since Russia seized it from Ukraine earlier this month.
Ukraine denounced the visit as a "crude violation" of international norms.
At a press conference in Crimea's capital, Simferopol, Mr. Medvedev announced plans to upgrade the Black Sea peninsula's social benefits, transportation, and infrastructure.
The prime minister said Russia will create a special economic zone in Crimea, offering incentives for business with lower taxes and simpler rules.
Mr. Medvedev, who is leading a delegation of top Russian government ministers, then traveled to Sevastopol, the Crimean port city where the Russia Navy's Black Sea Fleet is based.