(CNN) -- U.S. President Barack Obama didn't speak very long at the White House on Friday, but his message was clear: Russia should not use military force to change the fate of Ukraine.
"The United States will stand with the international community in affirming that there will be costs for any military intervention in Ukraine," Obama said.
The president made his remarks as events moved quickly in Ukraine, with troops believed to be from Russia moving into Crimea, the southern section of Ukraine that favors close ties with neighboring Russia. Other parts of Ukraine and the new government leaders want to align with Europe.
"We are now deeply concerned by reports of military movements taken by the Russian Federation inside of Ukraine," Obama 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.
"It would represent a profound interference in matters that must be determined by the Ukrainian people."
He said Ukraine must be autonomous.
"Throughout this crisis, we have been very clear about one fundamental principle: The Ukrainian people deserve the opportunity to determine their own future," he said.
Just before Obama spoke, the U.S. ambassador to the United Nations, Samantha Power, called for an "urgent international" mediation mission to Crimea.
Also, a bipartisan group of 12 senators from the Foreign Relations Committee expressed support for U.S. assistance in Ukraine and warned of Russian intervention.
"We do not seek confrontation with President Putin and his government, but simply to ensure that Russia abides by its commitments and adheres to core principles of international law. A peaceful, democratic, stable, and sovereign Ukraine is in our national interest," the senators wrote in a letter to Obama.
Vice President Joe Biden spoke with Ukrainian Prime Minister Arseniy Yatsenyuk on Friday to "reaffirm the United States' strong support for the new government and our commitment to the sovereignty, territorial integrity, and democratic future of Ukraine," a statement from the vice president's office said.
The State Department warned U.S. citizens Friday night to avoid non-essential travel to Ukraine, particularly to the Crimean Peninsula, citing instability.