US President Barack Obama has warned Russia there will be "costs" for any military intervention in Ukraine.
He said he was deeply concerned by reports of Russian military movements inside the country.
Ukraine's acting president has accused Russia of deploying troops to the Ukrainian region of Crimea and trying to provoke Kiev into "armed conflict".
Crimea's pro-Moscow prime minister has asked Russian authorities for help in maintaining peace in the region.
"I appeal to the president of the Russian Federation, Vladimir Putin, to provide assistance in ensuring peace and tranquillity on the territory of the Autonomous Republic of Crimea," Serhiy Aksyonov said in a statement.
Mr Aksyonov, who was appointed by the Crimean parliament on Thursday, also said he was taking control of Crimea's interior ministry, armed forces, fleet and border guards "on a temporary basis".
"All commanders are to obey only my orders and instructions," Mr Aksyonov said. "I ask all those who refuse to do so to resign."
The new cabinet in Ukraine is due to meet for the first time on Saturday to discuss the deepening crisis over Russia's reported military deployments.
Russia's UN ambassador earlier insisted any troop movements in Crimea were within an existing arrangement with Ukraine.
Overnight reports said armed men in unidentified military uniforms had seized another airfield.
On Friday they took over airports in the Crimean capital, Simferopol, and Sevastopol, where Russia's Black Sea Fleet is based.
Ukrainian media citing local officials said 13 Russian aircraft carrying nearly 2,000 suspected troops had landed at a military air base near Simferopol. The report remains unconfirmed.
Russian armoured vehicles and helicopters were also seen in and around Simferopol and Sevastopol.
Flights from and to Simferopol were cancelled with airlines saying airspace over the peninsula had been closed.
The armed men also moved in on Crimea's parliament, state television building and telecommunication centres.
Speaking from the White House, President Obama commended Ukraine's interim government for its "restraint".
"Any violation of Ukraine's sovereignty and territorial integrity would be deeply destabilising, which is not in the interests of Ukraine, Russia or Europe," he said.
"It would represent a profound interference in matters that must be determined by the Ukrainian people. It would be a clear violation of Russia's commitment to respect the independence and sovereignty and borders of Ukraine - and of international laws."
He added: "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."
Mr Obama did not spell out what any US response might be. However, the BBC's Beth McLeod in Washington says the US is considering exerting economic pressure by withholding the deeper trade ties that Moscow seeks.
It is also considering boycotting a G8 summit hosted by Russia, she adds, although that is not until June.
In a TV address on Friday, Ukraine's interim President Olexander Turchynov said Moscow wanted the new government to react to provocations so it could annex Crimea.
He appealed to Russian President Vladimir Putin to "stop provocations and start negotiations".
He said Russia was behaving as it did before sending troops into Georgia in 2008 over the breakaway regions of Abkhazia and South Ossetia, which have large ethnic Russian populations.
"They are implementing the scenario like the one carried out in Abkhazia, when after provoking a conflict, they started an annexation of the territory," Mr Turchynov said.
However, Russia's ambassador to the UN, Vitaly Churkin, said that any Russian military movements in Crimea were within Moscow's long-standing arrangement with Ukraine on the deployment of military assets.
"We are acting within the framework of that agreement," he said, after a closed-door meeting of the UN Security Council.
He did not give details of any Russian military deployment.
The Kremlin said President Putin had spoken of the "extreme importance of not allowing a further escalation of violence" during telephone conversations with Western leaders.
On Friday, Ukraine's former President Viktor Yanukovych made his first public appearance since being ousted from office a week ago.
Speaking in Russia, he apologised for not "having enough strength to keep stability" in Ukraine and called his usurpers "young, neo-fascist thugs".
Mr Yanukovych said he would "continue to struggle for the future of Ukraine", but said he would only return if his safety could be guaranteed.
Ukraine has started procedures demanding his extradition.
Mr Yanukovych is wanted on suspicion of mass murder following violent clashes between police and protesters last week that left more than 80 dead.
Ukraine's political crisis began in November when Mr Yanukovych rejected a trade deal with the EU in favour of a similar agreement with Russia.
The move brought thousands of Western-leaning protesters out on to the streets calling for his resignation and closer ties with the EU.
Since he was deposed, tensions have shifted to Crimea where the majority of the population are ethnic Russians.