PARIS — Unemployment in the eurozone rose to a new high in October, according to official data released Friday. But the head of the European Central Bank tempered the bad news by predicting that the region’s economy would begin to recover next year.

ECB president Mario Draghi cautioned that, ‘‘We haven’t gotten out of the crisis yet.’’ But he told Europe 1 radio in Paris, ‘‘The recovery for the entire eurozone will no doubt begin in the second half of 2013.’’