Last weekend's European parliament election and presidential election in Ukraine produced sharply contrasting results. Europe's voters expressed their dissatisfaction with the way that the European Union currently functions, while Ukraine's people demonstrated their desire for association with the EU. European leaders and citizens should take this opportunity to consider what that means – and how helping Ukraine can also help Europe.

The EU was originally conceived to be an ever-closer association of sovereign states willing to pool a gradually increasing share of their sovereignty for the common good. It was a bold experiment in international governance and the rule of law, aimed at replacing nationalism and the use of force.

Unfortunately the euro crisis transformed the EU into something radically different: a relationship of creditors and debtors in which the creditor countries impose conditions that perpetuate their dominance. Given the low turnout for the European parliament election, and if support for Italian prime minister Matteo Renzi's were added to the anti-EU vote on the left and the right, it could be argued that the majority of citizens are opposed to current conditions.

Meanwhile, just as Europe's bold experiment in international governance is faltering, Russia is emerging as a dangerous rival to the EU, one that has global geopolitical ambitions and is willing to use force. Putin is exploiting an ethnic national ideology to bolster his regime. Indeed, speaking on the Russian radio programme Direct Line last month, he extolled the genetic virtues of the Russian people. The annexation of Crimea has made him popular at home, and his effort to weaken America's global dominance, in part by seeking an alliance with China, has resonated favorably in the rest of the world.

But the Putin regime's self-interest is at odds with Russia's strategic interests; Russia would benefit more from closer co-operation with the EU and the US. And resorting to repression in Russia and Ukraine is directly counterproductive. The Russian economy is weakening, despite the high price of oil, owing to the flight of capital and talent. Using violence in Kiev's Maidan has led to the birth of a new Ukraine that is determined not to become part of a new Russian empire.

The success of the new Ukraine would constitute an existential threat to Putin's rule in Russia. That is why he has tried so hard to destabilise Ukraine by fostering self-declared separatist republics in eastern Ukraine. With the Donbas region's largest employer mobilising protests against the separatists, Putin's plan may not work, and he is now likely to accept the results of the presidential election, thereby avoiding additional sanctions. But Russia is likely to seek other avenues to destabilise the new Ukraine, which should not be too difficult, given that the security forces, having served the corrupt regime of the former president Viktor Yanukovych, are demoralised and not necessarily loyal to the new leadership.

All of this has happened very fast and very recently. Both the EU and the US are preoccupied with their internal problems and remain largely unaware of the geopolitical and ideological threat that Putin's Russia poses. How should they respond?

The first task is to counteract Russia's efforts to destabilise Ukraine. With the EU's "fiscal compact" and other rules limiting the scope of government assistance, innovative thinking is needed. The single most effective measure would be to offer free political risk insurance to those who invest in or do business with Ukraine. This would keep the economy running, despite the political turmoil, and it would signal to Ukrainians that the EU and the US – governments and private investors alike – are committed to them. Businesses would flock to a newly open and promising market if they were fully compensated for losses caused by political events beyond their control.

Political risk insurance may sound too complex to deploy quickly. In fact, insurance of this type already exists. Private insurers and reinsurers like Germany's Euler Hermes have offered it for years. So have government institutions, like the World Bank's multilateral investment guarantee agency and the US government's overseas private investment corporation. They must, however, charge substantial premiums to cover the cost of reinsurance.

Faced with high premiums, most businesses would simply opt to wait on the sidelines until the storm passed. That is why the governments concerned must take over the reinsurance function and use their agencies only to administer the insurance policies. They could guarantee the losses in the same way as they underwrite the World Bank: each government would provide a modest pro-rata capital infusion and commit the rest in the form of callable capital that would be available if and when losses are actually paid out.

The EU would have to modify the fiscal compact to exempt the callable capital and allow actual losses to be amortized over a number of years. Guarantees of this kind have a peculiar feature: the more convincing they are, the less likely they are to be invoked; the reinsurance is likely to turn out to be largely costless. The World Bank is a living example. By acting promptly and convincingly, the EU could save Ukraine – and itself. What I propose for Ukraine could also be implemented at home. As long as there are so many productive resources lying idle, it would make sense to exempt from the fiscal compact investments that would eventually pay for themselves. Renzi, for one, is advocating precisely this course of action.

Putin plans to turn Crimea into a showcase by lavishing more than €50bn (£41bn) on it in the next few years. With European support, Ukraine could compare favourably. And, if such an initiative marks the beginning of a growth policy that Europe so badly needs, by saving Ukraine Europe would also be saving itself.

• George Soros is Chairman of Soros Fund Management and the author of The Tragedy of the European Union

Copyright: Project Syndicate, 2014.