Barroso insists: Europe's crisis is not over yet

European Commission President Jose Manuel Barroso has told CNBC that although Europe's economy has turned the corner, it is not yet out of its crisis.

"How can we say that we are out of the crisis with these very high levels of unemployment?" he said at the World Economic Forum in Davos.

"At the same time, I think it fair to say that we have overcome some very important difficulties."

(Read more: Gloves off: Summers and Osborne slug it out over austerity)

The euro zone's economy grew by 0.1 percent in the third quarter of 2013, after emerging from the longest recession in continental Europe in over 40 years the previous quarter. Economic surveys for sectors including services and manufacturing appear to show that the recovery is gathering steam, with activity picking up in December.

Unemployment in the 17-member currency bloc, however, remains stubbornly high at 12.1 percent. While youth unemployment increased in November 2013, according to data released earlier this month, with 3.575 million under-25s without a job in the euro zone.

Jose Manuel Barroso
Eric Piermont | AFP | Getty Images
Jose Manuel Barroso

Barroso, who is the head of the European Union's executive arm, however, highlighted that the region's periphery in particular had performed much better than critics had feared.

"Instead of a Greek exit - now we have new members joining the euro zone," he said.

(Read more: France's Moscovici: We're not building the Soviet Union)

Ireland's successful exit from its bailout program, Spain's banking sector reforms and Portugal's successful austerity measures were also European success stories, he said.

"My message is we have turned a corner, but we are not yet out of a crisis - so let's keep the reform momentum so that we can address the real problem we have in Europe now: very high unemployment."

(Read more: Italy Fin Min: Recovery under way, but jobs will lag)

By CNBC's Katrina Bishop. Follow her on Twitter @KatrinaBishop and Google

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