PARIS — The euro zone economy grew slightly faster than expected in the last three months of 2013, an official report showed on Friday, bringing welcome news for the global economy amid signs of slowing in the United States and China.

Although growth in the 18-nation currency union is still weak, at a 1.1 percent annualized rate, it was the euro zone’s third straight quarter in positive territory, indicating that the bloc is well beyond the year-and-a-half recession that ended in mid-2013.

The broader 28-member European Union also grew, though weakly, for the third consecutive quarter. The Union, with a market of 500 million consumers and an economy worth about 11.7 trillion euros, or $16 trillion, is one of the pillars of the global economy, and the extended weakness there has been a major source of concern for officials in the United States.

Germany and France, the two largest euro zone members, led the upturn. The Netherlands broke out of recession, and the pace of growth picked up modestly in Portugal, Spain and Italy.