Analysts welcomed the figures, which reinforce other survey findings, but were also cautious as the debt crisis continues to sap the economy and unemployment runs at record highs.
The eurozone appears "on course for further modest growth in the third quarter but recovery looks like being a gradual process that will be vulnerable to any shocks," said Howard Archer of IHS Global Insight.
The economy of the 17-nation eurozone, home to about 340 million people, grew 0.3 per cent in the three months to June, the Eurostat statistics agency said in a second estimate.
In the full 27-member EU, the economy expanded 0.4 per cent in the second quarter, better than the initial 0.3 per cent reading and after shrinking 0.1 per cent in the first.
Compared with output in the second quarter 2012, the eurozone shrank 0.5 per cent while the EU was flat.
During the same period, the US economy grew 0.6 per cent compared with the first quarter and by 1.6 per cent compared with a year earlier.
Meanwhile a closely-watched business survey showed the key services sector in the eurozone returned to growth in August as overall business activity hit a 26-month high.
The data also showed that growth in the powerhouse Germany economy was not enough to stop employment levels falling while second-ranked France slipped back faster than in July.
At 50.7 in August, up from 49.8 in July, Markit said its separate PMI for the services sector which accounts for the bulk of economic activity showed growth for the first time in 19 months.
Manufacturing activity had already crossed the 50-points boom-or-bust line in July.
"Looking ahead, the hope for the eurozone is that currently rising confidence will encourage businesses to lift their employment and investment plans, and will also encourage consumers to spend more," Archer said.
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