LONDON (AP) - The eurozone's labor market appears to have stabilized, official figures indicated Tuesday, another sign that the eurozone economy is recovering from its longest-ever recession. Though Eurostat, the EU's statistics office, said the unemployment rate across the 17-member eurozone held steady at 12 percent in August, it found the number of people out of work fell for the third month running. That's the first time the region has enjoyed such a run since April 2011. In total, the number of unemployed dipped by 5,000 to 19.18 million, triggering hopes that the 20 million threshold that many economists had been forecasting this year will not be struck and that the 12.1 percent record high booked in June may not be breached. "The eurozone's jobless rate is past its peak for the current economic cycle," said Zach Witton, economist at Moody's Analytics. However, the unemployment rate will fall only gradually as the weak recovery provides limited support to profit margins, giving companies little incentive to boost hiring. As usually happens in a recovery, the modest improvement in the labor market has lagged the region's emergence from recession by a few months. The economy grew in the second quarter by a modest quarterly rate of 0.3 percent after contracting for six straight quarters, its longest recession since the euro currency was launched in 1999. Most surveys suggest the eurozone expanded further during the summer months and that the growth won't rely only on Germany, Europe's largest economy. Even Greece, mired in recession for the best part of six years as the global financial crisis morphed into a crippling sovereign debt crisis, is expected to start growing soon. Hopes for an improvement in the economy were supported by a closely-watched manufacturing survey released Tuesday. The purchasing managers' index for the manufacturing sector - a gauge of business activity published by financial information company Markit - was 51.1 points in September. Though down on August's 26-month high of 51.4, the survey points to continuing expansion - anything above the 50 threshold indicates growth. "This is good news for the eurozone but also for the global economy," said Chris Williamson, chief economist at Markit. The downturn in demand caused by the region's recession and the uncertainty generated by its debt crisis had cast a shadow over economic recoveries across the globe. But we must not get too carried away. Over the past three years, the eurozone has been the laggard of the world economy as it grappled with a debt crisis that at various times threatened the future of the euro currency itself. Countries across the region, but mainly in the south, such as Greece, Portugal and Spain, have had to enact tough austerity measures to convince bond market investors that they could get a handle on their public finances. A combination of recession, poor management and expensive bank bailouts had caused public debt to swell in the region. The problems afflicting the eurozone weighed on sentiment around the world, putting a brake on the global economic recovery. The eurozone, with its population of a little more than 500 million, is a key market for global firms seeking to do business. Though welcome, few economists think the eurozone's current economic growth is enough to significantly bring down unemployment, particularly among the young. The manufacturing PMI survey, for example, showed companies in the sector were still shedding jobs in September, though at a slower rate than before. The Eurostat figures also mask huge divergences across the eurozone: While Germany has an unemployment rate of 5.2 percent, Spain's jobless rate stands at 27.9 percent. The situation in Greece is even worse, with 27.9 percent of people out of work in June - Greek figures are compiled on a different timeframe. The situation among the young - that is, potential workers under the age of 25 - is even more acute. Greece and Spain, for example, have over half their youth unemployed. In Greece, youth unemployment stood at a stunning 61.5 percent in June. As well as being a burden to a country's coffers, sky-high levels of youth unemployment have an additional social cost of denying potential workers skills and experience - that's a long-term cost to the region's economic potential and has also fueled an increase in social tensions.