U.S. President Barack Obama said he is deeply concerned about reports of Russian military movements in Ukraine.
Speaking to reporters at the White House, he said "there will be costs" for Moscow if there is any Russian military intervention in Ukraine.
Obama said "we are now deeply concerned by reports of military movements taken by the Russian Federation inside of Ukraine."
Armed soldiers believed to be Russian took control of two airports in Ukraine's republic of Crimea early on the morning of February 28.
Several Russian military helicopters have been seen flying over the Crimean capital, Simferopol.
Meanwhile, Ukrainian acting President Oleksandr Turchynov has accused Russia of aggression in the Crimean peninsula and called on President Vladimir Putin to stop "provocations" and pull back military forces.
Turchynov said the Ukrainian military will fulfill its duty, but will not be drawn into provocations.
In televised comments, Turchynov also drew a parallel between the situation in Crimea and the brief 2008 war between Russia and Georgia.
Earlier on February 28, officials of Ukraine's new government accused Russian troops of launching an illegal military operation in Crimea and seizing the two airports.
A Ukrainian government official in Kyiv has also said that 13 Russian planes have landed at an airport in Sevastopol.
The official said the planes carried a total of some 2,000 soldiers. That report has not been independently confirmed.
Russian Ambassador to the UN Vitaly Churkin would not confirm or deny the reports of Russian soldiers involved in those actions at the airports or other places in Crimea.
Ukraine has offically protested to Russia over alleged violations of Ukrainian airspace by Russian aircraft in Crimean peninsula.
An Al-Jazeera reporter said some mobile phone and SMS access provided by UKRTelekom was not available in Crimea.
The reporter added that the local TV and radio station TRK Krim is surrounded by armed gunmen.
Russia's Black Sea Fleet, which is based in the Crimean port of Sevastopol, said all movements of its forces in Crimea were carried out in accordance with its basing agreement with Ukraine.
Churkin reiterated that claim to reporters at the United Nations.
The United Nations Security Council said it would hold a closed-door meeting on February 28 to discuss the crisis, in response to a request from Ukrainian authorities.
Reports on the evening of February 28 said civilian flights to Crimea's capital, Simferopol, had been cancelled due to the closure of the airspace over the peninsula. It was not immediately clear who had closed the airspace or why.
In its protest to Moscow, Ukraine's Foreign Ministry said there had been violations of Ukrainian airspace in Crimea, and said Russia had violated the lease terms for the Black Sea Fleet.
The Kremlin said Putin had discussed the crisis with British and German officials, and had warned against any further escalation of violence.
Ukrainian National Security Council head Andriy Parubiy accused the Russian military of "illegally conducting" operations in Crimea.
"We know the fact that there are members of the Russian Black Sea fleet operating in disguise and illegally conducting their actions on Ukrainian territory in the Republic of Crimea," he said. "The National Security and Defense Council [of Ukraine] has measures developed to neutralize this scenario."
In Washington, White House spokesman Jay Carney reiterated U.S. warnings that it would be "a grave mistake" if Moscow intervened militarily.
"Reports of Russian intervention in Crimea are of deep concern to the United States, and as Secretary [of State John] Kerry said and [U.S. National Security Adviser Susan] Rice has said, intervention would be a grave mistake," he said. "These reports are also inconsistent with Russia's previous statements to the United States that Russia will respect the territorial integrity of Ukraine."
On February 28, pro-Russian demonstrators gathered outside the regional parliament building in Simferopol and prevented Ukrainian national parliament deputy Petro Poroshenko from entering, calling him a "traitor."
Poroshenko had traveled to Simferopol in an effort to defuse the tensions.
Vitali Klitschko, head of the Ukrainian Democratic Party for Reform, criticized the many Russian State Duma deputies who have traveled to Crimea in recent days to support the region's ethnic Russian population, including ultranationalist Vladimir Zhirinovsky.
"It looks very strange to me to see deputies of the Russian State Duma are coming to Crimea in such big numbers as some kind of a mass operation," Klitschko said. "I don't really understand what their goal is."
The media-freedom representative of the Organization for Security and Cooperation in Europe (OSCE), Dunja Mijatovic, issued a statement condeming the presence of armed people at the offices of state television in Simferopol.
Reports said about 20 armed people had taken up positions outside the building, but reports say they have not directly interfered with journalists.
In another development, the Russian Foreign Ministry said the Russian Consulate in Simferopol would start issuing Russian passports to former members of Ukraine's disbanded Berkut riot police, which played a role in the recent deadly clashes with protesters in Kyiv.
With reporting by Reuters, Interfax, and AFP