However, Russian President Vladimir Putin told German Chancellor Angela Merkel in a phone call Monday that some troops were being withdrawn from the Ukraine border, Merkel's office said. The withdrawal involved a battalion of about 500 troops, Russian news reports said.
The U.S. reacted cautiously to the Russian troop movement, with Secretary of Defense Chuck Hagel saying that "tens of thousands" of Russian forces still remained along the Ukrainian border, a situation he called "a tremendous buildup."
The new government in Ukraine said the action only increased its uneasiness about Russia's intentions.
"We have information that Russia is carrying out incomprehensible maneuvers on the border with Ukraine," Ukrainian Foreign Ministry spokesman Yevgen Perebyinis said. "Troops in some places are moving backward, some of them are moving forward. Which is why, obviously, we are worried by these movements of armed forces. We have no clear explanation from the Russian side about the aim of these movements."
Russian Foreign Minister Sergey Lavrov and U.S. Secretary of State John Kerry also discussed Ukraine by phone Monday, a day after holding talks in Paris, the ministry said.
A senior U.S. official said Lavrov had promised Kerry that a division of Russian troops would be pulled back; a division generally consists of thousands of troops.
"Now there have been reports of possible drawdowns of Russian military forces from the border. We haven't seen that yet, but if they turn out to be accurate, that would be a good thing," said White House spokesman Jay Carney.
Concerns of a possible invasion of eastern Ukraine — home to many ethnic Russians — were stoked by the large numbers of troops Russia had along the Ukrainian border for what Moscow said were military exercises.
One Russian battalion — about 500 troops — that had been sent to the Rostov region next to Ukraine was being withdrawn to its permanent base in the central Samara region, Russian news agencies quoted the Defense Ministry as saying Monday.
Alexander Rozmaznin, deputy chief of the Ukrainian armed forces command center, confirmed a drop in Russian troop numbers along the border.
In Kiev, meanwhile, Ukraine's acting president flatly rejected escalating Russian pressure to turn Ukraine into a loose federation.
"Russia's leadership should deal with problems in the Russian Federation, and not with Ukraine's problems," Ukraine's acting president Oleksandr Turchinov said. "It is Ukrainians that should dictate the form of the new constitution and how the country is structured."
Medvedev, who led a delegation of Cabinet ministers on a surprise visit to Crimea, pledged that Russia will quickly boost salaries and pensions there and pour in resources to improve education, health care and local infrastructure.
But making no mistake about Russia's view of the peninsula, Deputy Prime Minister Dmitry Rogozin tweeted a photo of himself upon arrival with the words "Crimea is ours, and that's that."
Russia annexed Crimea from Ukraine in March after a hastily called referendum held just two weeks after Russian forces had taken control the Black Sea region. Ukraine and the West have rejected the vote.