As Ukraine's interim leaders work to restore stability, U.S. Defense Secretary Chuck Hagel, speaking at a meeting of NATO defense ministers in Brussels, Belgium, urged all parties to avoid "provocative actions" in Ukraine.
And he warned that the United States was keeping a sharp eye on Russia in light of its recent moves.
"I'm closely watching Russia's military exercises along the Ukrainian border," he said. "I expect Russia to be transparent about these activities, and I urge them not to take any steps that could be misinterpreted or lead to miscalculations."
This, he said, "is a time for very calm, wise leadership on the Russian side, on everyone's side here."
U.S. officials earlier told CNN that the Russian military exercises were making U.S. military and intelligence agencies concerned that Russia may be positioning ground forces to be able to move across the border into Ukraine if Moscow issued such orders.
Russian Defense Minister Sergey Shoigu has said the exercises are being conducted to check "combat readiness."
U.S. Secretary of State John Kerry said his Russian counterpart, Foreign Minister Sergey Lavrov, offered reassurances Thursday that military exercises were previously scheduled and not related to Ukraine.
"We believe that everybody now needs to step back and avoid any kind of provocations, and we want to see in the next days ahead obviously that the choices Russia makes conform to this affirmation that we received today," he said after a phone conversation with Lavrov.
"We are also making the same point about reducing tensions in the Crimea to the Ukrainians. It is very important that the process continue in a thoughtful and respectful way."
In Simferopol, it was not immediately known who was occupying the government buildings. Mohyliov, the Crimean Prime Minister, told CNN earlier Thursday that the gunmen had refused to speak with him, telling him he had no authority.
The men, who stormed the building early Thursday, had made no demands, and it was not clear what they wanted, he said.
He added that government security forces, which were outside the buildings, would not use force or weapons to take over the buildings.
"All police in Ukraine have been ordered to be prepared," acting Interior Minister Arsen Avakov wrote on his Facebook page. "Orders have been issued to create a cordon around the Parliament in Crimea and to avoid shooting and violence."
A witness, who gave his name only as Maxim, said he saw the armed men run into the building and kick out police. "Nobody knows what is going on inside at the moment. We only saw the building being taken over," he said. He said the men took bags containing antitank weapons, sniper rifles, assault rifles and handguns from buses into the building.
Anders Fogh Rasmussen, NATO's secretary general, described the seizure of the regional government administration building and parliament as "dangerous and irresponsible."