* U.S. manufacturing jumps in Jan, ISM at 53.1, a 9-month high * China's official PMI eases to 50.4, HSBC reading at two-year high * Euro zone PMI suggests worst may be over * Economists still expect subdued global growth By Steven C. Johnson and Jonathan Cable NEW YORK/LONDON, Feb 1 (Reuters) - U.S. manufacturing growth quickened in January and hiring across the economy increased in late 2012, but Chinese factories only managed a slight rebound as the new year began, suggesting that world economic growth remains sluggish. The euro zone economy, meanwhile, likely contracted again at the end of last year, though surveys on Friday suggested the worst of the region's downturn may be over. Surveys conducted by the financial information firm Markit and the Institute for Supply Management both showed U.S. manufacturing grew in January at its fastest clip in nine months, boosted by a surge in domestic demand. The data "suggests the underlying health of the industrial sector continues to improve and rising production will help the economy return to growth in the first quarter, providing there are no set-backs in coming months" said Markit chief economist Chris Williamson. On Thursday the U.S. government reported the economy contracted in the fourth quarter for the first time since the recession ended three years ago, although analysts said there was no reason for panic because consumer spending and business investment picked up.. Separate data showed U.S. employers added 157,000 jobs in January and 127,000 more than initially reported in November and December, suggesting the sluggish recovery remained on track. "This shows that underneath the surface, the fourth-quarter economy was really pretty good despite all the defense cuts. I think the private sector is leading the way," said Jack Ablin, chief investment officer at BMO Private Bank in Chicago. U.S. and European stocks moved higher after the data, with the benchmark U.S. S&P 500 stock index coming off its best monthly performance since October of 2011. UNEVEN RECOVERY IN ASIA, EUROPE Some analysts worried, however, that nearly $100 billion of U.S. governemnt spending cuts set to take effect in March could crimp U.S. economic growth unless Congress acts to delay them. The nature of the recovery on factory floors across Asia and Europe was more uneven. Surveys showed growth slowed in India and stalled in South Korea while Britain's expanded modestly. Two separate versions of China's purchasing managers' index (PMI) pointed to rising factory output in the world's second-biggest economy but at very different speeds, suggesting a bumpy recovery from China's worst downturn in 13 years. China's official PMI released by the government eased to 50.4 from 50.6 in December, while a similar PMI from banking group HSBC rose to a two-year high of 52.3. Both showed export orders either grew marginally or shrank as shoppers in the United States and Europe, the two biggest buyers of Chinese goods, reduced spending. Domestic demand, on the other hand, was the main force behind China's gentle economic rebound. "The general sense, if you look at what it is in the pipeline, is that we will be getting a little bit more activity in the months to come," said Peter Dixon, an economist at Commerzbank. "The Chinese economy does appear to be gaining a bit of traction but not a huge amount (and) the euro zone numbers tell us the economy remains stuck in low gear." Even so, signs of improvement in Chinese, European and Japanese data suggested the global economy was "gradually" improving, New York Federal Reserve President William Dudley said on Friday. WORST OVER FOR EUROPE? Euro zone factories did post their best month in nearly a year, thanks to an improved outlook in Germany. With the euro zone PMI at an 11-month high of 47.9, some economists said the worst of the downturn may be over. Total output in the 17 countries that use the euro still probably shrank by 0.4 percent in the final three months of 2012, which would be the third straight quarter of contraction, according to a Reuters poll published last month. "While still in contraction territory, the manufacturing PMIs signal that upward momentum is spreading and the pace of contraction in euro zone output is slowing," said Evelyn Herrmann, European economist at BNP Paribas. But she said the divergence in growth rates between core and peripheral countries as well as between Germany and France suggests recovery remains fragile. Markit said the gap between the German and French PMIs was the widest ever, leaving Germany, Europe's largest economy, as the region's shining light. Germany's PMI staged its biggest one-month jump since the middle of 2009 to 49.8, while the PMI for France, Europe's second-largest economy, sank to a four-month low of 42.9. British manufacturing expanded modestly in January as output grew at the fastest pace since September 2011, offering a small boost to an economy flirting with recession. Factories in Indonesia, the star emerging economy of the past year, said business shrank in January from December for the first time in eight months, while manufacturers in Taiwan reported the fastest growth in 10 months.