Russia has pulled out a motorised infantry battalion from a region near Ukraine's eastern border, the Russian Defence Ministry said.
Monday's statement said the battalion was heading back to its permanent base in Russia's Samara region after completing training. The statement did not make clear whether other troops near the border would be pulled back.
Russian President Vladimir Putin told German Chancellor Angela Merkel that he had ordered a partial withdrawal of Russian forces from the region, the Merkel said in a statement.
US Secretary of State John Kerry told his Russian counterpart Sergey Lavrov on Sunday that progress on resolving the Ukraine crisis depended on a troop pullback from the border.
Earlier on Monday, Ukraine's Defence Ministry said there had been a gradual withdrawal of Russian troops from its border.
"In recent days, the Russian forces have been gradually withdrawing from the border," Oleksiy Dmytrashkivskiy, Ukraine's Defence Ministry spokesman, told AFP news agency.
US and EU officials estimated over the weekend, that Russia's sudden military buildup along Ukraine's eastern frontier had reached between 30,000 and 40,000 soldiers.
Kiev's Centre for Military and Political Studies analyst Dmytro Tymchuk said on Monday that his sources had told him Russia had only 10,000 soldiers remaining near the border by Monday morning.
The Ukrainian Defence Ministry official said Kiev had not been formally notified of the drawdown by Moscow and therefore did not know why the troops were being moved.
"This could be linked to a regular rotation of soldiers," said Dmytrashkivskiy. "Or it may be linked to the Russian-US negotiations."
Crimea economic zone
In Crimea, Russian Prime Minister Dmitry Medvedev announced on Monday that Moscow would declare the peninsula as a special economic zone with tax incentives to attract investors, according to Reuters news agency.
He made the announcement during his visit to the former Ukrainian region.
Crimean officials have said their economy is facing a shortfall and needs economic stimulus from Russia.
Medvedev promised to raise the level of salaries for municipal employees and pensions to average Russian levels and to modernise the region's hospitals.
"As a result of joining Russia, not one resident of Crimea, not one resident of Sevastopol should lose anything. They can only gain," Medvedev said during the special cabinet meeting.
Local officials, including Crimean Prime Minister Sergei Aksyonov, were also present at the meeting that was broadcast on Russian state television.