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President Barack Obama said Friday that “there will be costs to any military intervention in Ukraine,” after Russian military forces reportedly entered that country’s Crimea region.

“Any violation of Ukraine’s sovereignty and territorial integrity would be deeply destabilizing,” Obama said at the White House, saying the United States is “deeply concerned” about the reports of the Russian presence there.

“The Ukrainian people deserve the opportunity to determine their own future,” he said, adding that interference would be "a clear violation of Russia's commitment to respect the independence and sovereignty and borders of Ukraine and international laws."

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U.S. officials told NBC News that the costs could include a boycott of a G-8 meeting that Russia is to host and costs to Russia's economy.

U.S. officials confirm to NBC News that uniformed Russian forces are still entering Simferopol in Ukraine’s Crimea region. While not able to confirm the numbers used by Ukraine officials -- 2,000 or more -- the officials say they have no reason to doubt the basic information that there are Russians arriving on Russian aircraft.

A U.S. official said that Obama would not have issued the warning if U.S. intelligence wasn't sure Russian forces have moved into Ukraine. But the official said Obama didn't want to be more specific to allow Russian President Vladimir Putin room to back down.

The Obama administration has repeatedly warned Russia not to inflame tensions in Ukraine by intervening in the volatile country.

Obama’s remarks come after deposed Ukrainian president Viktor Yanukovych pledged to “keep fighting” the new leaders of the country. Yanukovych, who has resurfaced in Russia, blamed the West for “irresponsible policies” and “pandering to” to protesters who occupied Kiev.

House Speaker John Boehner said in a statement, "Both the administration and the European Union have a responsibility to work together to maximize the economic and political pressure on Russia to withdraw its troops."

Republican Majority Leader Eric Cantor said in a statement that there should be "sanctions against Russian individuals and entities who use force or interfere in Ukraine's domestic affairs."

— Carrie Dann, Andrea Mitchell, Chuck Todd and Robert Windrem