AP) — European leaders insist they want to keep Greece in the Eurozone, but are putting off any agreement on how they hope to accomplish that. Greece says it, too, wants to stay in the Eurozone, but until after elections it’s uncertain whether it can implement the austerity that Europe has set as a condition for doing so.

Essentially, both are playing for time – about a month. The question is whether financial markets will wait or force their hand.

Concerns that European leaders lack the political will – and wherewithal – to tackle the continent’s economic problems have worried the markets for weeks. Among the 17 countries that use the euro, seven are in recession. Business confidence is under pressure and banks are feeling the squeeze. The biggest fear is that if Greece cannot be kept in the euro, other larger economies – like Spain or Portugal – might face the same fate.

“The breakup of the Eurozone will be a disaster. Greece could leave, and others could leave, and this would be a huge financial tsunami,” said Dariusz Kowalczyk, senior economist at Credit Agricole CIB in Hong Kong. “Europe is not doing enough, and the market may not wait for them.”

Greece has gone through round after round of massive spending cuts and tax hikes to slash its deficit and rein in its debt in exchange for the international bailout loans that help it pay the bills. But the country is now in its fifth year of recession, and many argue it cannot hope for a recovery if it sticks to the deal. And Greeks – though still keen to remain in the single currency club – are calling for better terms or, at least, for the pace of austerity to be slowed down.

In a general election this month, neither of Greece’s two main parties, both of which support the bailout deal, fared well. Instead, minor parties that are threatening to renege on those commitments saw their popularity surge. A new round of elections is set for June 17.

If the Greeks pick an anti-bailout government the second time round and renege on the terms of the bailout, the flow of funds will be stopped and the country could be forced into a messy exit from the euro bloc as it has no other choice but to print its own currency to pay its way.

That could cause a deeper fracture the euro – other debt-stricken Eurozone members, such as Spain and Portugal, might also fall victim to market fears that they could be next in line for collapse – and rattle global financial markets.

There had been hope that this week’s Brussels summit would have seen a softening in the rest of the Eurozone’s stance with Greece, extending, for example, the deadline for some of its reforms and cuts.

Some European countries are already hinting that Greece should be given better terms. Both the International Monetary Fund and the Organization for Economic Cooperation and Development, which monitors economic trends in developed economies, also are pushing for the demands on some countries to be eased.

However, as their summit in Brussels broke up early Thursday morning, the leaders failed to offer any reprieve to struggling Greece. Instead they reiterated that they continued to support Greece’s Eurozone membership – provided it stuck to the terms of the bailout deal.

Manuel Barroso, President of the EU’s executive Commission, told a post-summit press conference: “We stand by Greece. We expect that Greece also stands by its commitments.”

European Council President Herman van Rumpoy echoed the sentiment: “Continuing the vital reforms to restore debt sustainability, foster private investment and reinforce its institutions is the best guarantee for a more prosperous future in the euro area.”

Some politicians have already begun to factor in a Greek exit, however. In a frank admission that Greece could wind up abandoning the euro, Luxembourg Prime Minister Jean-Claude Juncker told reporters that the Eurozone countries “have to consider all kinds of events,” but insisted that “the working assumption” was that Greece would remain part of the euro.

The European leaders aim to have more concrete proposals for strengthening the region at their next summit on June 28-29, but before then Greece will have held its elections, by which time Europe’s financial system may have already been pushed to the brink.

French investment bank Credit Agricole’s research analysts said EU leaders had set the expectations bar very low for the summit “and yet they managed to disappoint nervous markets.”

Shares on the Athens Stock Exchange hit a new 22-year low Thursday, closing down 4.53 percent despite gains made elsewhere in Europe.

There are concerns among investors that uncertainty over Greece’s future in the Eurozone could spark a run on the country’s banks, further destabilizing the already-shaky banking system and pushing the country even quicker towards a chaotic exit from the currency.

Greeks have been steadily withdrawing deposits in recent months. Bank of Greece figures show that total household and business deposits stood at about (EURO)165 billion ($207.2 billion) in March 2012, compared to (EURO)235 billion ($295.1 billion) in October 2009, just before the crisis broke. Meanwhile some (EURO)700 million ($879 million) were withdrawn in the week following the inconclusive May 6 election.

The summit also addressed the issue of whether the risk inherent in some countries holding so much debt should be spread across the entire Eurozone – issuing so-called “Eurobonds.” This would mean every country could borrow funds at the same rate, substantially lowering the costs for the more indebted countries. French President Francois Hollande wants the bonds to finance growth projects and ease concerns about weaker countries’ debt, but Germany’s Angela Merkel refuses to consider such an option.

“It would have been great news,” said Oscar Moreno of Madrid brokerage Renta4. “It would have been good if there had at least been agreement to study it. It would have calmed things down and been a very preliminary first step to the idea of a Eurobond. But we got nothing.”

Economists say Eurozone leaders have to find another way to increase its defenses than offering bailout after bailout to its debt-stricken members. Javier Diaz-Gimenez, a professor of economics at IESE Business School in Madrid, said that the Eurozone needs a fundamental redesign.

“The solution has to be some change in design,” Diez-Jimenez said. “Something that says, `OK, these were the things that were missing.

“Just staggering on, that is not going to work. If you keep staggering on, you are eventually going to fall.”