The Russian Defense Ministry said Monday that a motorized infantry battalion is returning home after taking part in military exercises along the Ukrainian border.

Russian President Vladimir Putin also told German Chancellor Angela Merkel in a telephone call that he had ordered a “partial withdrawal” of troops, according to Merkel’s office. Russian Foreign Minister Sergei Lavrov also informed Secretary of State John F. Kerry of the withdrawal.

In Washington, however, officials said they could not confirm that any Russian troop movement had taken place.

“I cannot confirm . . . one way or the other whether the Russians are pulling troops back,” Defense Secretary Chuck Hagel told reporters, saying that the Russian force on Ukraine’s border numbers in the “tens of thousands.”

White House press secretary Jay Carney said that “we’ve seen reports, and if they are true . . . that would be a positive sign, because it is certainly something that we have explicitly called for.”

President Obama signed an executive order in March authorizing financial sanctions affecting several major sectors of the Russian economy, including the energy industry, if Russian forces enter Ukraine beyond Crimea.

On Monday, Carney said that the United States and European allies will never recognize Russia’s annexation of Crimea. He said travel bans and asset freezes against Russian individuals close to Putin, imposed last month when the Crimea takeover began, will not be lifted until Russian forces in that region are withdrawn.

“We will not recognize Russia’s illegal occupation of Crimea. We do not and we will not, and our European partners and allies and others have made that clear,” Carney said.

Ukrainian officials said they were aware that Russia is pulling some troops back from the border after a month of nerve-rattling maneuvers adjacent to eastern Ukraine, but in Kiev, the Ukrainian capital, a Foreign Ministry spokesman said he believes that other Russian troops are being rotated in.

A battalion can range in size from a few hundred to about 1,500 soldiers. The United States has said that Russia has 40,000 troops taking part in the exercise on the border.

The Russian Defense Ministry said the battalion is returning to its home base in the Samara region, along the Volga River.

Russia has maintained from the start of the crisis that it is conducting only legal, routine military training and has no intention of extending its reach beyond Crimea. But Ukrainian, U.S. and European officials have warned that an incursion could take place at any moment — and that, at the very least, the Russian activity appears designed to put pressure on Kiev’s fledgling government.

German Foreign Minister Frank-Walter Steinmeier said the reported troop reduction seemed to be “a small signal that the situation is becoming less tense,” the Reuters news service reported.

Kerry and Lavrov met in Paris on Sunday to discuss the Ukraine crisis but reached no agreement. “We have some ideas. We have proposals that both sides made,” Kerry said, but he acknowledged that the United States cannot force Russia to pull back its forces from the border area.

The United States has demanded that Russia withdraw its troops, open talks with the Ukrainian government and agree to international monitoring in Ukraine and Crimea.

Russia has proposed a new federal system in Ukraine that would give its eastern and southern regions broad autonomy over economic and other matters. The Ukrainian government has rejected the Russian proposals as a back-door way to seize control of portions of the country beyond Crimea.

DeYoung reported from Washington. Anne Gearan, traveling with Kerry, and Ernesto Londoño in Washington contributed to this report.