* Flash euro zone PMIs post unexpected declines in March * Most survey responses came before Cyprus bailout deal news * U.S. manufacturing growth, hiring quickens * Chinese manufacturers ramp up production By Jonathan Cable and Steven C. Johnson LONDON/NEW YORK, March 21 (Reuters) - Economic malaise in the euro zone deepened in March even before Cyprus ran into debt trouble, but manufacturing in the United States and China improved, surveys showed on Thursday. Solid growth in the United States and China, the world's largest economies, will be important for overall global growth, particularly as the 17-country euro zone continues to struggle. Markit's Flash Eurozone Composite Purchasing Managers' Index, seen as a reliable economic growth indicator for the bloc, fell more than expected, to 46.5 in March from 47.9 in February. The index has now been below the 50 mark that separates growth from contraction for all but one of the past 19 months. Most responses to the survey were received before Cyprus's parliament rejected a bailout that included an unprecedented levy on all bank deposits, leaving the country perilously close to financial collapse. "The sharp decline in the flash composite PMI in March pours cold water on hopes of an imminent end to the euro zone recession," said Martin van Vliet, economist at ING. "If the situation surrounding Cyprus spirals out of control, the onset of recovery might well be delayed." French businesses had their worst month in four years, likely pushing the euro zone's second-biggest economy into recession. Germany, the bloc's biggest economy, also showed signs of fatigue. Things were a bit sunnier in the United States and Asia. Markit's Flash U.S. Manufacturing Purchasing Managers Index rose to 54.9 this month from 54.3, and the pace of hiring in the sector increased. "With manufacturing a reliable bellwether of the rest of the economy, gross domestic product will have risen at a much improved rate" over the first three months of 2013, Chris Williamson, chief economist at Markit, said. The U.S. economy grew at a 0.1 percent rate in the fourth quarter of 2012, but economists are forecasting a first-quarter growth rate of about 2 percent. A separate report from the Philadelphia Federal Reserve Bank showed factory activity in the mid-Atlantic region grew in March. The survey is seen as one of the first monthly indicators of the health of the U.S. manufacturing sector. Another hopeful sign for the United States: sales of existing homes hit a three-year high in February and prices rose. The data suggests a recent acceleration in the housing market recovery continued. The four-week average of Americans filing for first-time jobless benefits fell to its lowest level in five years. The data "continue to point toward improvement in U.S. labor markets," said Citigroup economist Steven Wieting. In China, factories increased their output after a holiday dip, suggesting solid, if not spectacular, first-quarter growth for the world's No. 2 economy. The HSBC China PMI for March rose to 51.7 from 50.4, but remained below a two-year high reached at the start of the year. The pullback in February had raised concerns in financial markets that China's recovery was losing steam. Government data earlier in March suggested the economy had started 2013 with only tepid growth after a burst in the fourth quarter. The HSBC report allayed some of those fears. "Current readings ... seem to us to be consistent with (gross domestic product) growth close to 8 percent year-on-year," wrote Dariusz Kowalczyk of Credit Agricole-CIB in Hong Kong. WORSE TO COME? In Europe there were few signs of a brightening outlook. Markit said conditions in Europe could worsen by the end of the month. "Events that hit business confidence can have a very rapid effect on the data, and so there is good reason to believe that responses we collect this week will on average be more negative," Williamson said, referring to the Cyprus confusion. The latest PMI data, which already showed a contraction since the second quarter of last year, suggested the euro zone economy would shrink 0.3 percent in the current quarter, Markit said. That outlook is worse than the 0.1 percent contraction predicted in a Reuters poll last week that also forecast negligible growth next quarter. Germany's composite PMI fell in March, although it held above 50 for a fourth month, suggesting some strength in Europe's largest economy. Some of the factory activity in the euro zone was generated by running down order books while incoming new business for services firms dropped at the fastest pace since October, suggesting next month's PMI will also be weak.