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.
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."
Mr Obama did not spell out what any US response might be. However, a BBC correspondent reports 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, although that is not until June.
Ukraine's interim Prime Minister, Arseniy Yatsenyuk, said Kiev would not "give in to Russian provocation". He was speaking at the first meeting of his cabinet, installed after the overthrow of President Viktor Yanukovych.
Mr Yatsenyuk 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 Sergiy Aksyonov has asked Russian authorities for help in maintaining peace in the region.
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".
Ukraine's defence minister said on Saturday that Russia had "recently" brought 6000 additional personnel into Ukraine and that the Ukrainian military were on high alert in the Crimea region. Reuters reports that Ihor Tenyukh gave no further details in comments to reporters in Kiev.
Russia's UN ambassador earlier insisted any troop movements in Crimea were within an existing arrangement with Ukraine.