Russian President Vladimir Putin ratcheted up the military pressure on the new Ukraine government today as he ordered military exercises near the border with Ukraine.
Elsewhere, anti-Russian groups have held rallies in the capital of Crimea region in Ukraine.
The United States has warned Russia that it would be a "grave mistake" to embark on military intervention in Ukraine.
"I don't think there should be any doubt whatsoever that any kind of military intervention that would violate the sovereign territorial integrity of Ukraine would be a huge - a grave mistake," US Secretary of State John Kerry said.
BREAKING: Kerry says US plans $1 billion in loan guarantees for Ukraine.
Secretary of state John Kerry has said that the US is not looking for confrontation with Russia over the Ukraine.
Kerry urged Russian President Vladimir Putin to be "very careful" in his judgments over the situation in Ukraine and that the two nations need not get into a "Cold War" stand-off over the country.
Nato defence ministers have issued a statement supporting Ukraine's sovereignty and territorial integrity today.
"A sovereign, independent and stable Ukraine, firmly committed to democracy and the rule of law, is key to Euro-Atlantic security," the ministers said in a statement issued during a meeting in Brussels.
"Nato allies will continue to support Ukrainian sovereignty and independence, territorial integrity, democratic development, and the principle of inviolability of frontiers, as key factors of stability and security in central and eastern Europe and on the continent as a whole," they said.
Russian Defence Minister Sergei Shoigu said the country was taking measures to ensure the security of facilities and arsenals of its Ukraine-based Black Sea naval fleet, state broadcaster Ria reports.
Russia said that Ukrainian extremists are "imposing their will" and whipping up religious tension after the ousting of President Viktor Yanukovich.
In a statement, the Foreign Ministry said that priests and property of a church affiliated with the Russian Orthodox Church had faced threats, and warned that the religious tension could cause "an even greater schism in Ukrainian society."
Defence Secretary Philip Hammond said the UK would "take note" of any activities by Russian forces, and said there should be no external interference in Ukraine.
Russian president Vladmir Putin ordered an urgent drill to test the combat readiness of the armed forces across western Russia this morning, state news agencies reported.
Defence minister Sergei Shoigu said:
"In accordance with an order from the president of the Russian Federation, forces of the Western Military District were put on alert at 1400 (1000 GMT) today."
Putin has ordered various surprise drills across Russia since he returned to the presidencey in 2012, saying it was important for the military to be kept on its toes.
Russian Deputy Foreign Minister Sergei Storchak said a solution to Ukraine's economic crisis must be found quickly, but that no multilateral talks on the issue had started yet.
He told Reuters that if there were any talks on a financial package for Ukraine, they were only taking place at a national level at the moment, and that high-level international groups of experts had yet to be formed.