In a statement issued by the White House, Obama said his administration is in daily communication with Russian officials, "and we've made clear that they can be part of an international community's effort to support the stability and success of a united Ukraine going forward, which is not only in the interest of the people of Ukraine and the international community, but also in Russia's interest."
"However, we are now deeply concerned by reports of military movements taken by the Russian Federation inside of Ukraine," he said. "Russia has a historic relationship with Ukraine, including cultural and economic ties, and a military facility in Crimea, but any violation of Ukraine's sovereignty and territorial integrity would be deeply destabilizing, which is not in the interest of Ukraine, Russia, or Europe."
Obama said a Russian military intervention would "represent a profound interference in matters that must be determined by the Ukrainian people."
"It would be a clear violence of Russia's commitment to respect the independence and sovereignty and borders of Ukraine, and of international laws," the president said. "And just days after the world came to Russia for the Olympic Games, it would invite the condemnation of nations around the world. And indeed, the United States will stand with the international community in affirming that there will be costs for any military intervention in Ukraine."
He said Vice President Biden spoke Friday with Ukrainian Prime Minister Arseniy Yatsenyuk and assured him "the United States supports his government's efforts and stands for the sovereignty, territorial integrity and democratic future of Ukraine."
Uniformed men carrying weapons stood guard outside the Simferopol airport Friday in the pro-Russia Crimea region of Ukraine, but reports conflicted on whether they controlled the facility and who they were, CNN said.
Dozens of armed men seized government administration buildings in Simferopol, the Crimean capital, Thursday and raised a Russian flag. Later, in a vote of no-confidence, pro-Russian members of the Crimean Parliament dismissed the government of Anatolii Mohyliov, perceived as pro-Kiev.
Ousted former Ukrainian President Viktor Yanukovych said Friday he will fight for Ukraine's future and said Russia should intervene, in a way that wouldn't "violate the integrity of Ukrainian sovereignty," the Washington Post said.
"It would not be correct on my part to say what Russia needs to do," Yanukovych said. "But Russia cannot stand aside, it cannot be indifferent to the destiny of such a big partner as Ukraine.
"Russia needs to use all the leverage it has to prevent the chaos and terror in Ukraine," said Yanukovych, whose decision in November not to sign political and trade agreements with the European Union in favor of closer ties with Russia led to anti-government protests. "It's hard for me to give any kind of tips. I do not accept any attempt at intervention that would violate the integrity of Ukrainian sovereignty.
"I believe that Russia will act," he said. "Since I know the character of Vladimir Vladimirovich Putin, I am surprised he has kept silent. This is a big question."
Yanukovych -- speaking in public for the first time since he left Kiev last week -- told reporters in the Russian city of Rostov-on-Don he was forced to leave Ukraine because of threats against him and his family, RIA Novosti reported.
He said he does not recognize the authority of the Verkhova Rada, Ukraine's parliament.
Before his news conference, Ukraine's chief prosecutor asked Russia to extradite Yanukovych, wanted by his country on mass murder charges, RIA Novosti said.
On its website, the prosecutor's office said it "intends to raise the issue of extradition of Viktor Yanukovych, an internationally wanted citizen of Ukraine."
Ukraine placed Yanukovych on an international wanted list after filing mass murder charges against him for his role in the deadly clashes between police and anti-government protesters in Kiev in which more than 80 people died in the days before the agreement was signed and he was deposed.
The opposition took control of Parliament Feb. 22 and, along with members of Yanukovych's ruling Party of Regions, voted to impeach Yanukovych, who fled Kiev and arrived at a military facility in Rostov Thursday.
The impeachment vote came the day after Yanukovych and opposition parties signed an agreement to end the escalating violence in Kiev and elsewhere. The agreement called for formation of a unity government, early elections and constitutional reforms.
Yanukovych said he hasn't met Putin since he arrived in Russia.
"When I ended up in Russia, I had a phone call with him," Yanukovych said. "We agreed once the president of Russia has an opportunity, we will meet, but I don't know when this will happen."
Yanukovych said he was in Rostov-on-Don because he had a friend who lives near there, the Post said.
Crimean lawmakers scheduled a referendum on greater autonomy for the region for May 25, the day Ukraine is to hold its presidential and local elections.
In Kiev, Ukraine's Parliament demanded Russia halt activity that may be interpreted as attacking Ukraine's sovereignty and end support for separatist actions.
Newly appointed Ukrainian Interior Minister Arsen Avakov said on his Facebook page Russia's actions in Crimea were tantamount to "an armed invasion and occupation" and "a direct military provocation on sovereign Ukrainian territory."
Since Yanukovych's departure from power following violent protests last week, the divide among Ukrainians has widened. Those in western Ukraine generally support the country's interim government and its leaning toward the European Union while those in the east are more pro-Russia.
U.S. Defense Secretary Chuck Hagel warned Thursday against any provocative acts by any party.
U.S. Secretary of State John Kerry said Russian Foreign Minister Sergei Lavrov had told him the military exercises had already been scheduled and had nothing to do with events in Ukraine. Kerry said Lavrov reaffirmed a commitment given by Putin that Russia would "respect the territorial integrity of Ukraine."
The Ukrainian Parliament, which includes members of Yanukovych's party, named Yatsenyuk as prime minister Thursday.
Yatsenyuk said Ukraine didn't want a fight with Russia but wouldn't accept the secession of the Crimea region.
Crimea "has been and will be a part of Ukraine," said Yatsenyuk, 39, who served as economy minister and parliamentary speaker before Yanukovych took office in 2010.