US President Barack Obama says Russia is "on the wrong side of history" in Ukraine and its actions violate international law.
Obama told reporters in the Oval Office today that the United States is considering economic and diplomatic options that will isolate Russia.
The President called on Congress to work on an aid package to Ukraine and make it the "first order of business."
Obama said continued military actions in Ukraine "will be a costly proposition for Russia."
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Meanwhile any Russian ultimatum to Ukraine threatening a possible attack would be a "dangerous escalation'' of the tensions in Crimea, a US official has said.
Washington was working to find out if Moscow has demanded Ukrainian leaders surrender or face an all-out assault, as claimed by the Ukraine military.
Ukraine's military said that Russia had given its forces an ultimatum to surrender in Crimea or face an all-out assault on the strategic Black Sea peninsula that has been overrun by Kremlin-backed troops.
But Russia's Black Fleet swiftly denied any such demand and the country's parliament speaker said there was no need yet for Moscow to use its "right'' to launch military action in Ukraine.
The reports of an ultimatum "if true, in our view constitute a dangerous escalation of the situation, for which we would hold Russia directly responsible,'' said State Department spokeswoman Jen Psaki.
Read more of the Herald's Ukraine coverage today:
• Putin must back down, says Key
• Ukraine: 10 things you need to know
• Symbolic acts of defiance in face of Russian threat
• Editorial: Riposte must hurt Russia, help Ukraine
"The ultimatum is to recognise the new Crimean authorities, lay down our weapons and leave, or be ready for an assault,'' regional Ukrainian defence ministry spokesman Vladyslav Seleznyov told AFP in the Crimean capital Simferopol.
"It may be at 1:00 am, 2:00 am, 3:00 am (Tuesday). There are different times,'' he said.
Ukraine accused Russia of pouring more troops into Crimea as world leaders grappled with Europe's worst standoff since the Cold War and financial markets plunged on fears of an all-out conflict.
Russian Foreign Minister Sergei Lavrov said forces were needed in the flashpoint Black Sea peninsula until "the stabilisation of the situation" in the ex-Soviet nation and lashed out at Washington's "unacceptable threats" against Moscow.
Crimea - the strategic host to tsarist and Kremlin navies since the 18th century - has been under de facto occupation by Moscow-backed forces since President Vladimir Putin won parliament's authorisation on Saturday to send troops into Ukraine.
The new leaders in Kiev branded the move a declaration of "war" and jittery global markets sank on Monday over fears of a conflict while the price of oil surged.
The Moscow market alone at one stage lost 13 per cent on a Black Monday of trading that saw the ruble hit historic lows.
World leaders were holding a series of urgent meetings and telephone conversations to try to avert a conflict and also to help Ukraine avert a possible catastrophic debt default.
The European Union was trying to overcome differences on how to respond to the escalating crisis on its eastern edge, with hawkish ex-Soviet satellites pushing for sanctions but others including heavyweights France and Germany calling for soft diplomacy.
British Foreign Secretary William Hague warned Russia of "consequences and costs" as he met Ukraine's Western-backed but untested interim leaders in Kiev.
The world's richest nations have already threatened to strip Moscow of its coveted seat at the Group of Eight for menacing its ex-Soviet neighbour.
But Europe and Washington appear to have limited options in dealing with Putin - a veteran strongman with mass domestic appeal who has cracked down on political freedoms and appears more interested in rebuilding vestiges of the Soviet Union than repairing relations with the West.
Ukraine has soared to the top of the global agenda even as the brutal conflict in Syria rages and talks on Iran's nuclear drive enter their most sensitive stage.
"This cannot be a way in the 21st century to conduct international affairs," Hague told reporters. "It is not an acceptable way to behave and there will be consequences and costs."
The crisis threatens to blow up into the biggest test to global diplomacy since the fall of the Berlin Wall in 1989.
It first erupted in November when protests began against the pro-Kremlin regime over its scrapping of an EU pact and culminated in a week of carnage last month that claimed nearly 100 lives and saw the downfall of president Viktor Yanukovych - now living in exile in Russia.
"There was the (1962) Cuban missile crisis and the Soviet Union's decision to send tanks into Prague (in 1968). But in that era, we were effectively in a state of war," said Alexei Malashenko of the Carnegie Moscow Centre.
Germany offered a rare glimmer of hope by announcing that Putin had agreed in telephone talks with Chancellor Angela Merkel Sunday to set up a contact group on Ukraine.
Western allies in NATO also said they wanted to send international observers to Ukraine while engaging Moscow in direct talks.
Washington added it would like to see a mission from the Organisation for Security and Cooperation in Europe (OSCE) deployed in the nation of 46 million "immediately".
But EU foreign ministers were also considering the possibility of one day adopting punitive measures against Russia that included an arms embargo should the Kremlin fail to calls its troops back to their Crimean bases.
- 'All Ukraine bases blocked' -
Russia offered no immediate response to any of the proposals - all backed by interim leaders in Kiev who are trying to pull Ukraine closer to the European Union after replacing the Yanukovych regime.
Crimea is now almost under complete control of Russian forces and local pro-Moscow militia who patrol both government buildings and the perimeters of Ukrainian barracks on the rugged Black Sea peninsula.
"All military bases in Crimea are blocked," regional defence ministry spokesman Stanislav Seleznyov told AFP.
"All of the bases in Crimea are still under Ukrainian control. But they are surrounded."
The precarious situation for Kiev's new leaders was underscored on Sunday when Ukrainian navy commander Denis Berezovsky announced just a day after his appointment that he was switching allegiance to the pro-Russian authorities in Crimea after troops surrounded his building and cut off the electricity.
Crimea's pro-Kremlin government chief Sergiy Aksyonov - appointed on Thursday after an armed raid on the region's government building but who is not recognised by Kiev - immediately named Berezovsky as head of the peninsula's own independent navy.
- Black Monday in Moscow -
The first business day since Russian senators authorised Putin to use force saw markets stretching from Asia to Europe and New York nosedive and the Moscow exchange ended the day down nearly 11 per cent.
Russia's central bank unexpectedly hiked its main interest rate to 7.0 per cent from 5.5 per cent in a bid to halt a meteoric ruble decline that saw it hit record lows again the dollar on Monday.
"A situation is emerging that could have profound circumstances for many major Russian companies," Moscow's Nord Capital financial advisory said in a research note.
Shares in Russia's natural gas giant Gazprom tumbled by over 12 per cent on uncertainty about whether the state-controlled company may be ordered to halt deliveries to Ukraine - and by consequence Western Europe - as a punitive step by the Kremlin against the new Kiev team.
- IMF and Kerry in Kiev -
The White House released a statement symbolically signed by the G7 biggest industrialised nations - an economic grouping that unlike the G8 excludes Moscow - promising "strong financial backing" in a programme overseen by the International Monetary Fund.
An IMF team was due to arrive in Kiev on a 10-day fact-finding mission that will weigh the merits of the new Ukrainian government's request for $15 billion in assistance this year.
Kerry warned ahead of his arrival in Kiev on Tuesday that Moscow risked losing its G8 seat over its "brazen act of aggression" in Ukraine.
Washington is under under particular pressure because it is bound together with Britain - and Russia - to protect Ukraine's territorial integrity by a 1994 agreement that saw Kiev gave up its Soviet-era nuclear arms.