Kiev's attempts to reassert control – which saw it launch a military operation and retake the town of Kramatorsk on Tuesday – may have drawn praise and support from the White House, but they've led to heightened concerns of violence.
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"Ukraine could well decide to push ahead with its military action, because of the support it is enjoying at the moment – from the U.S. explicitly," Lilit Gevorgyan, CIS analyst at IHS Global Insight, told CNBC.
"But even if Ukraine manages to supress an uprising in the east, we could still see a rise in social unrest in the coming months. These eastern regions are unmodernized; they don't fit well with Europe but do with Russia."
A key moment in the developing crisis will be the meeting of the European Union (EU), U.S., Ukraine and Russia, due to take place in Geneva on Thursday.
"A lot will depend on the outcome of the discussions," Gevorgyan said, stressing that it was a good sign that - despite the military action by Ukraine - Russia had decided not to boycott the meeting.
"It indicates that Russia is not eager to launch itself into the east and expand its hold in the region," she added.
One possible outcome of the talks could be agreement on how the four powers will oversee Ukraine's constitutional reform and presidential elections on May 25.
Gevorgyan said a peaceful resolution to the situation was crucial for both Ukraine -- which relies on Russia for its energy supplies and orders for its exports -- and Russia, which has invested heavily in Ukraine and has significant business interests there.
The U.S. and EU have already imposed travel bans and asset freezes on a number of Ukrainian and Russian officials, with Moscow retaliating by imposing sanctions of its own. But the West has threatened further sanctions this week if Moscow does not de-escalate the crisis.
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"The Ukraine crisis is a wake-up call to the EU. We don't live in some post-modern la-la land, there are external treats… we need a much more vigorous response," Philippe Legrain, author of "European Spring" and former economic advisor to the president of the European Commission, told CNBC.
"We need a much more severe sanctions, asset freezes targeted at Putin and his cronies in the Kremlin… We need to see the bigger picture here: the post-Cold War order is at risk."
But although the West could add to its current restrictions against Russian officials, more severe sanctions look unlikely.