The 17 nations that use the euro will see their economies shrink 0.1% this year, before showing weak growth of 0.9% next year, the OECD predicts.
This compares with 2.4% growth in the US economy this year, with 2.6% predicted for 2013.
The OECD also backed calls from some Europeans to combine cuts in spending with measures to boost growth.
“The crisis in the Eurozone remains the single biggest downside risk facing the global outlook,” commented OECD chief economist Pier Carlo Padoan.
Late last year, the organisation predicted a “deep recession with large negative effects for the global economy” if the Eurozone did not tackle the crisis.
On Tuesday, it said: “The immediate dangers of such developments have receded somewhat since last autumn, although the dangers have not disappeared.
“Failure to act today could lead to a worsening of the European crisis and spill-overs beyond the Eurozone, with serious implications for the global economy.”
‘Growth-friendly’
The OECD seems to be backing calls from the new French president to pass measures such as “increasing European Investment Bank funding for infrastructure projects”.
They also said that “better use” could be made of the European Central Bank’s balance sheets and called for “a further easing in the euro area”.
“Fiscal consolidation and structural measures must proceed hand in hand, to make the adjustment process as growth-friendly as possible,” the OECD said.
The jobless rate is currently 10.9%, the maximum since the euro was formed in 1999. With further increases predicted in the jobless total this is likely to fuel the backlashes against austerity.
“Elections in a number of euro-area countries have signalled that reform fatigue is increasing and tolerance for fiscal adjustment may be reaching a limit,” said OECD chief economist Pier Carlo Padoan.
“Rising unemployment and social pain may spark political contagion and adverse market reaction”, with countries outside the euro also at risk of being hit, he added.
The OECD is an organisation that consists of 34 countries, including the US and Western European nations.
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