US President Barack Obama on Tuesday said Russia was not "fooling anybody" over the crisis in Ukraine after Vladimir Putin denied that Russian forces were operating on the flashpoint Black Sea peninsula of Crimea.

In a show of support for the new interim leaders in Kiev, visiting US Secretary of State John Kerry condemned Russia's "act of aggression" and accused Moscow of "working hard to create a pretext for being able to invade further".

Pro-Kremlin forces are in de facto control of the strategically crucial, majority-Russian Crimean peninsula where Ukrainian troops remain blocked inside their barracks in the worst standoff between the West and Russia since the end of the Cold War.

But world financial markets rebounded Tuesday as traders interpreted comments by Putin that force was "a last resort" as a sign that tensions in Europe's largest country were easing.

There was further relief when Ukraine's interim Prime Minister Arseniy Yatsenyuk announced his government had made the first "timid" contacts with Russian leaders aimed at resolving the crisis.

"So far, (the talks) have been rather timid. But the first steps have been made," Yatsenyuk said in a statement after talks with Kerry.

Obama said the European Union and allies like Canada and Japan all believed Russia had violated international law by mobilising troops following the ouster of pro-Kremlin president Viktor Yanukovych.

"President Putin seems to have a different set of lawyers, maybe a different set of interpretations. But I do not think that is fooling anybody," Obama said during a visit to a school in Washington DC.

Putin, breaking over a week of silence with a press conference in Moscow, said his country reserved the right to use "all available means" in the crisis. "This is a last resort," he added.

He rejected claims that Russian forces were operating in Crimea, saying that only "local forces of self-defence" were surrounding Ukrainian military bases in the region.

Asked if Russian forces took part in operations in Crimea he said, "No, they did not participate," adding: "There are lots of uniforms that look similar."

When told of Putin's remarks by a reporter in Kiev, Kerry responded: "He really denied there were Russian forces in Crimea?" and shook his head, bewildered.

The top US diplomat also laid flowers and lit a candle at the scene of memorials to the nearly 100 people who died on Kiev's Independence Square last month.

The square was the focal point of three months of protests sparked by Yanukovych's decision to reject a key EU deal in favour of closer ties with Moscow.

During Kerry's visit, the US confirmed $1 billion in loan guarantees to help shore up Ukraine's debt-laden economy.