Eurozone's return to normal operations is also set to be patchy, with some of the member economies doing better than others, a report by Moody's Analytics said.
The EU has 27 members but Eurozone comprises only 17 of them, many among them struggling to stay afloat and dependent on bailouts from Brussels, financed by European taxpayers, and additional handouts from the International Monetary Fund.
The eurozone's continuing malaise worries non-members such as Britain, who are in dispute with European Union bigwigs in Brussels over decisions that are likely to hurt financial services industries. European plans to tax financial transactions once they pass through a relevant EU zone also worry North American financiers, in particular Wall Street.
Moody's Analytics said eurozone's short-term outlook improved recently, "but high levels of public and private debt continue to weigh on consumption and investment in many countries."
"Euro Zone Outlook: The Burden of Debt" said the improved short-term outlook for the eurozone reflects that its GDP unexpectedly increased 0.3 percent in the second quarter of 2013.
Germany grew 0.7 percent from the first quarter and France 0.5 percent, while output declined 0.2 percent in Italy and 0.1 percent in Spain, said the report, citing preliminary estimates.
Germany's Spiegel Online magazine Friday leaked a report saying Greece was in line to receive another bailout soon after the German election Sept. 22, in which Chancellor Angela Merkel is hoping to get re-elected.
Growing doubts also mar analyses of eurozone member Spain's recovery prospects, Spiegel Online said.
"Measures to pull Spain out of the crisis are failing to bear fruit and exacerbating social tensions. While some are optimistic, the core problems remain, and many are questioning the old elite's ability to clean up the financial sector and reform the country."
The Moody's analysis said of the four biggest eurozone economies, only Germany and France are set to grow, while most of the currency union's southern members remain in recession.
"The recovery is long overdue and appears modest at best. Fundamental problems still need to be addressed. The high levels of public and private debt in the eurozone resulting from the sovereign debt and banking crisis remain a key concern," report author Petr Zemcik said.
"High debt weighs on growth, making households less likely to borrow and spend, reducing corporate investment and restraining government spending. Restructuring both public and private balance sheets may be the only solution for countries affected by high levels of debt," Zemcik added.
The report said excessive volumes of old debt impede the flow of new credit necessary to finance future growth, particularly in Spain, Italy, Portugal and Greece.
The banks' plight, in turn, stems from their fiscally weak governments, which are unlikely to be able to back financial institutions in trouble.
The problem could be alleviated if the eurozone moved more aggressively toward a regional banking union, with a common deposit insurance scheme, recapitalisation fund and a clear region-wide restructuring mechanism. But Germany has resisted such proposals to date, pushing instead for a less centralized system.
Improving economic conditions in some parts of the world may soon favor higher debt yields, which will raise borrowing costs and affect currency exchange rates.
The U.S. rates could rise as the Federal Reserve Board moves to slow its purchases of long-term debt, which in turn could push up the yields on European government bonds. This would likely push the euro lower against the U.S. dollar, the report warned.
Although eurozone's economy started to grow in this year's third quarter it is still expected to end the year 0.5 percent smaller than it began. It will take until 2015 for output to return to 2008 levels, the report said.
"The eurozone's growth will mainly be driven by increased demand from the [United States] and emerging economies," Moody's said. "A slowdown in these markets is the main risk to the outlook, along with any deterioration in the eurozone's internal situation."