European stocks closed much higher on Tuesday, after Russian President Vladimir Putin reassured markets and citizens that any use of force in Ukraine would only be a last resort.
The pan-European FTSEurofirst 300 Index provisional closed higher by 2 percent at 1,344.52 points, bouncing back from Monday's sharp declines.
Putin gave a muted response when asked about any potential conflict in Ukraine, at a Moscow press conference on Tuesday morning. He said there was "no need yet" to exercise Russian authority in Ukraine, and said he was not considering annexing Crimea .
Late on Tuesday, Ukrainian Prime Minister Arseny Yatseniuk said that his government and the Russian administration had opened talks on the crisis.
Meanwhile, U.S. Secretary of State John Kerry arrived in Kiev on Tuesday and announced economic assistance for Ukraine, in a show of support for its new government.
(Follow our live blog: Ukraine crisis: Latest news and market reaction)
Russia's MICEX Index led global markets higher, provisionally closing up by around 5 percent, after losing nearly $60 billion in market capitalization on Monday.
Ukrainian stocks also gained, with Kiev's UAX Index rising 9 percent.
Meanwhile, U.S. stocks also jumped on Tuesday, with the Dow and bouncing back after their worst hit in a month.
(Read More: Putin ends army exercise, Russian markets rally )
Christopher Granville, co-founder and managing director of the Russia team at Trusted Sources, told CNBC: "Why is it that markets are rebounding today? I think because financial markets always respond to uncertainty. Where might this end? Might the Russian army go on from the Crimea to invade eastern Ukraine or possibly the whole of Ukraine? Clearly the signals are now that is not the aim."
Glencore shares rise
In other stocks news, mining giant swung to a net loss in 2013 but reported earnings that were better than forecast; shares closed higher by 1.7 percent.
Germany's energy firm posted its first annual loss in six decades on Tuesda,y caused by nearly $7 billion in writedowns. However, shares rose 2 percent, with analysts saying that the results were better than expected.
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