WASHINGTON — President Barack Obama said Friday that he is “deeply concerned” by reports Russia had sent troops into Ukraine’s Crimea region and warned that “there will be costs” for any such military intervention.

“It would be a clear violation of Russia’s commitment to respect the independence and sovereignty and borders of Ukraine, and of international laws,” Obama said. “And just days after the world came to Russia for the Olympic Games, it would invite the condemnation of nations around the world.”

Uniformed men with automatic weapons appeared at airports in the Crimea on Friday morning and were seen patrolling streets in armored vehicles. But the identities of the men and their origin was unclear. Their uniforms bore no identifying insignia.

But Ukrainian officials in Kiev said the men were Russian troops. The men did not disrupt operations at the airport, but by nightfall, airspace over the Crimea was reported to have been closed. There were also reports that telecommunications between the Crimea and the rest of Ukraine had been cut after armed men destroyed cables.

Ukraine Interior Minister Arsen Avakov described the gunmen as an armed invasion.

Obama’s remarks came after ousted Ukrainian President Viktor Yanukovych resurfaced in Russia and said he remained his country’s legitimate elected leader. Russian President Vladimir Putin said Friday that any military activities taking place in Ukraine were routine and were not intended to threaten the nation’s sovereignty or incite further violence.

Obama said Russia’s involvement could be “deeply destabilizing” to Europe and represent “a profound interference” in Ukraine.

“The events of the past several months remind us of how difficult democracy can be in a country with deep divisions,” he said. “But the Ukrainian people have also reminded us that human beings have a universal right to determine their own future.”

Obama decided to address the growing crisis in Ukraine from the White House Briefing Room late Friday despite conflicting statements about what has taken place in Crimea, an area of southern Ukraine that was part of Russia until 1954, when Soviet Premier Nikita Kruschev transferred it to Ukraine when both Russia and Ukraine were part of the Soviet Union. The region is largely Russian speaking, and Russia maintains a major naval base there at Sevastopol, from which Russian troops could easily have traveled to the rest of Crimea.

Amateur video footage posted online purportedly showed Russian Mi-24 Hind gunships and Mi-8 Hip helicopters in airspace over the Crimea. The videos could not be independently verified.

“I don’t think anyone knows exactly what is going on,” said Anton Fedyashin, a Russia expert who directs the Initiative for Russian Culture at American University in Washington. “They are sending a signal without knowing what the hell is going on.”

The United States has repeatedly sought to downplay any rivalry with Russia over Ukraine, but the two nations have a complicated relationship that has been frayed in recent years by Putin’s penchant for undermining the United States at key moments, such as allowing fugitive NSA leaker Edward Snowden refuge from U.S. criminal charges.

The State Department is fond of reminding Moscow that the United States turned over hundreds of suspected criminals to Russia, and that the two governments worked closely in the Boston Marathon bombing investigation. But the countries are on opposite sides of the conflict in Syria, and long before the Ukraine crisis flared, few analysts still took seriously the Obama administration’s idea of a “reset” in U.S.-Russia relations. There was never much reciprocity from the Kremlin.

On Capitol Hill, lawmakers of both parties followed Obama’s lead, criticizing Russia and calling for an aggressive U.S. response.

“We need strong American and European leadership now to forestall any further threats to international peace and stability,” said House Majority Leader Eric Cantor, R-Va. “Russia’s leaders must understand that military intervention and further interference in Ukraine’s affairs are unacceptable and would result in significant consequences for Russia.”

In a letter to Obama, a dozen members of the Senate Foreign Relations Committee expressed support for U.S. assistance to Ukraine through loan guarantees.

“We also believe that the U.S. should make use of the tools at its disposal, including targeted sanctions; and asset recovery targeting corruption, to dissuade individuals who would foment unrest to undermine Ukraine’s territorial integrity or employ coercive economic measures against the Ukrainian people and the new Ukrainian government,” according to the letter.

Steven Bucci, director of the Douglas and Sarah Allison Center for Foreign and National Security Policy at the Heritage Foundation, said military action is not a viable option for the U.S.

“Beyond diplomatic and public condemnation, there is little that the U.S. can do,” he said. “President Obama has no particularly useful credibility to move the Russians. The lack of decisive action in the past, the failure of the so-called ‘reset,’ and the debt owed Putin for rescuing Obama’s dysfunctional Syria policy now give little or no moral or diplomatic leverage. We are likely to be an impotent bystander in the tragedy that could be unfolding.”

Last week, the Obama administration slapped visa restrictions on 20 senior Ukrainian officials to punish “the full chain of command” behind the bloody crackdown on a protest camp in Kiev. The visa sanctions represent the toughest U.S. action yet after three months of clashes between the Yanukovych government and protesters unhappy over the government’s decision in November to forgo a trade deal with the European Union in favor of a $15 billion bailout from Russia.

A senior administration official who spoke on condition of anonymity because of the sensitive diplomacy, said the U.S. is consulting with its European partners and considering how to respond. “It’s hard to see how we and other European leaders would attend the G-8 in Sochi if Russia is intervening in Ukraine,” the official said.

Obama spoke to Putin a week ago, and their administrations have been in daily contact. Vice President Joe Biden, who has been intimately involved in the talks, spoke to Ukrainian Prime Minister Arseniy Yatsenyuk to assure him that the U.S. supports his government.

Secretary of State John Kerry has spoken with his Russian counterpart, Sergey Lavrov, four times in the past six days — including a phone call Friday — as the administration has watched Russia’s maneuvering near the border with Ukraine.

Kerry called Lavrov on Friday morning to discuss then-emerging reports of Russian military activity in the Crimea, State Department spokeswoman Jen Psaki told reporters.

“He stressed, as he mentioned this morning, that the United States has concerns that all parties avoid any steps that could inflame tensions,” Psaki said of the exchange. “And he made very clear during that call that any intervention in Ukraine would be a grave mistake.”

Hannah Allam and Lesley Clark of the Washington bureau contributed to this report.