US President Obama has urged Russia to stop "intimidating" Ukraine and cut the number of troops it has on its border.
Russia is believed to have massed a force of several thousand troops close to Ukraine's eastern frontier.
Mr Obama told CBS News it may "be an effort to intimidate Ukraine, or it may be that [Russia has] additional plans."
Meanwhile, a Russian security official has said intelligence measures are being stepped up to counter Western threats to Moscow's influence.
"There has been a sharp increase in external threats to the state. The lawful desire of the peoples of Crimea and eastern Ukrainian regions is causing hysteria in the United States and its allies," Interfax quoted Alexander Malevany, deputy head of the Federal Security Service (FSB), as saying.
He said Russia was taking "offensive intelligence measures" to counter Western efforts to "weaken Russian influence in a region that is of vital importance to [Moscow]," Interfax reported.
Earlier, ousted Ukrainian President Viktor Yanukovych called for a national referendum to determine each region's "status within Ukraine".
He fled to Russia last month after massive demonstrations against him and clashes between protesters and police in which more than 100 people died. The Kremlin says the new government in Kiev came to power illegally.
President Obama, in the CBS interview recorded before he left Italy on Thursday, said President Vladimir Putin had been "willing to show a deeply-held grievance about what he considers to be the loss of the Soviet Union".
But he warned that the Russian leader should not "revert back to the kinds of practices that were so prevalent during the Cold War".
"I think there's a strong sense of Russian nationalism and a sense that somehow the West has taken advantage of Russia in the past, " Mr Obama said. "What I have repeatedly said is that he may be entirely misreading the West. He's certainly misreading American foreign policy."
Mr Obama said the US has "no interest in circling Russia" and "no interest in Ukraine beyond letting Ukrainian people make their own decisions about their own lives."