Also left unresolved was what Europe should do to spark economic growth and restore the confidence of investors, who have driven some countries' borrowing costs to unsustainable levels. The fiscal austerity agenda that Germany has promoted as the solution to Europe's problem of too much government debt has been met with rising skepticism in other euro countries.
The leaders of the 27 EU countries agreed to give institutions such as the European Investment Bank the task of drawing up proposals for growth in time for another summit in June. But there was discord over more aggressive actions promoted by some leaders heading into the summit, such as issuing bonds jointly as a way of reducing borrowing costs for heavily indebted nations among the 17 countries that use the euro.
The perception that European leaders lack the political will to tackle the continent's financial and economic problems has left markets on edge for weeks. Recession is spreading. Banks are under pressure. The biggest fear is that if Greece cannot be saved, other larger economies—like Spain or Portugal—might face the same fate.
The euro countries "have to consider all kinds of events," Luxembourg Prime Minister Jean-Claude Juncker told reporters after a European Union summit, but insisted that "the working assumption" was that Greece would remain part of the euro. Leaders gathered in Brussels recognized that Greece had endured significant hardships and promised to release development funds aimed at spurring growth.
But the statement from Juncker, who also chairs meetings of eurozone finance ministers, was a frank admission that Greece could wind up abandoning the euro. The country's fringe political parties, which are threatening to renege on commitments made to secure bailout loans, saw their popularity surge in recent elections. No party has been able to form a government, and the country will vote again June 17.
Many analysts have said that Greece, already in its fifth year of recession, has no hope of recovery if it sticks to the spending cuts and tax hikes it agreed to in order to secure bailout loans.
"We want Greece to remain in the euro area," German Chancellor Angela Merkel said after the meeting. "We expect that they will stick to the commitments that they have entered into."
Political uncertainty in Greece is just one of the fires the Europe needs to put out. Leaders are also worried about rising borrowing costs in Spain and Italy that could force them to seek bailouts, just like Greece, Portugal and Ireland did.
Markets had expected the latest EU summit to disappoint and it did. Europe's stock markets had fallen heavily during trading on Wednesday and the euro hit a near two-year low against the dollar.
Asian stock markets retreated Thursday as the lack of a breakthrough in Europe unnerved traders. Japan's benchmark Nikkei 225 was down 0.5 at 8,514.53 and Hong Kong's Hang Seng slipped 0.6 percent to 18,682.38.
Dariusz Kowalczyk, senior economist at Credit Agricole CIB in Hong Kong, said Thursday: "Europe is not doing enough, and the market may not wait for them."
One of the biggest questions facing Europe is whether it's time to cut Greece some slack. Some European countries seemed ready to ease the pressure, and international organizations have called for the pace of austerity measures to be slowed in some struggling countries.
But Thursday's summit of 27 European Union leaders ended with no apparent concessions. A final statement said Greece had to respect its commitments and trumpeted the money the eurozone and the International Monetary Fund had loaned Greece as a sign of their "solidarity." It did say that funds for economic development would be sent to Greece—though it's unclear how much of an immediate impact on growth they would have.
Juncker insisted early Thursday that he had not asked the euro nations to prepare national contingency plans for a possible chaotic departure of Greece from the currency.
French President Francois Hollande said that to evoke the even the possibility was dangerous—and would send a signal to the markets that the eurozone wasn't standing behind Greece.
The debate reflects the fine line European leaders must walk between pressuring Greece to stick to a program of spending cuts and tax hikes that have exacerbated its economic slowdown and trying to ensure its presence in the eurozone.
Spanish Prime Minister Mariano Rajoy suggested the European Central Bank resume some of its emergency measures, such as buying the bonds of weak countries, which has the impact of lowering countries' borrowing rates. The ECB has suspended the purchases because, as an independent body, it does not want to be seen supporting governments directly. Instead, it has given European banks massive amounts of cheap loans to bolster confidence in the financial system and allow banks to buy up their country's debt.
Leaders on Thursday also addressed the contentious issue of whether the countries that use the euro should spread the risk and borrow money jointly - 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.
Hollande has pushed for them as an important way to ensure such a crisis never happens again, but Merkel has rejected them, fearing they would reduce the pressure on heavily indebted governments to heal their finances and force Germany to borrow at higher rates.
Don Melvin contributed to this story.