Ukraine says Russian forces controlling Crimea have demanded the surrender of two warships, a claim Russia strenuously denied.
As the crisis deepened top U.S. legislators called for sanctions on Russia, including measures targeting banks and officials. President Obama said the U.S. was examining economic and diplomatic steps to isolate Moscow, and he called on Congress to expedite assistance for Ukraine.
Ukrainian Defense Ministry spokesman Maksim Prauta said four Russian navy ships were blocking Ukraine's anti-submarine warship Ternopil and the command ship Slavutych in Sevastopol's harbor.
He said the Russians ordered the crew to surrender within the hour or face Russians storming and seizing the ships and crew.
Interfax also quoted an unnamed source in the Ukrainian Defense Ministry earlier on Monday as saying a deadline to surrender at 0300 GMT had been set by the Black Sea Fleet's commander.
The same news agency later quoted an unnamed representative at the fleet's headquarters as saying no assault was planned, adding: "This is complete nonsense.''
The State Department said the reports, if true, would be "dangerous escalation" for which it would hold Russia responsible.
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Fears of a tit-for-tat campaign of economic sanctions between Russia and Western powers over Ukraine ratcheted up as the tensions rose, with concerns largely centering on Russia's supplies of natural gas to Europe.
But with the situation in Ukraine still fluid, it's not clear how far either side is willing to go. While the European Union is by far the biggest consumer of Russian gas, any disruption would come at huge financial cost to Moscow.
"The world now faces a new round of geopolitical tension with potentially very high stakes," said Jane Foley, an analyst at Rabobank International.
Sen. Chris Murphy (D-Conn.), chairman of the Senate's Europe subcommittee, told Reuters the U.S. Senate is considering sanctions, among them travel bans and asset freezes, though he also noted that the US had to work with Europe for the sanctions to be effective.
House Speaker John Boehner (R-Ohio) also told the Cincinnati Enquirer it was time for sanctions, though he did not elaborate on the form they should take.
Diplomatic efforts continued, as the European Union called on Russia to withdraw its troops to bases and hold consultations with Kiev, while extending the possibility of holding a summit of EU leaders to discuss the crisis in Ukraine.
The EU's foreign policy chief Catherine Ashton told reporters after emergency talks among EU foreign ministers on the crisis that she "anticipated'' the EU to convene a summit on the issue this week. That summit was later scheduled for Thursday.
In a Monday afternoon public meeting of the UN Security Council, Russia's UN ambassador Vitaly Churkin argued his country's actions were "fully appropriate and legitimate." He added that Russian President Vladimir Putin had a written request from Ukraine's ousted president to use the Russian military to defend the country.
US ambassador Samantha Power, in her statement, decried Russia's "self-serving" statements and said its entry into Crimea "is not a consensual intervention ... it is an act of aggression."