BEIJING, (Reuters) - Activity in China vast factory sector shrank for a third consecutive month in May as export orders contracted at the sharpest rate in nearly two years, a private survey showed on Monday, suggesting China remains locked in an economic cooldown.

The final HSBC/Markit Purchasing Managers' Index (PMI) stood at 49.2 in May, below the 50-point level that separates an expansion from a contraction in activity on a monthly basis.

That is little changed from a preliminary reading of 49.1, and up a touch from April's 48.9.

In a sign that China's sputtering economy could face bigger headwinds in the short-term, a sub-index for new exports skidded to 46.7, a low unseen since June 2013, and well below April's 50.3.

Factory output also shrank for the first time this year as the sub-index slipped under 50.

"A solid fall in new export work contributed to fewer new orders, which in turn led to the first contraction of output in 2015 so far," said Qu Hongbin, an economist at HSBC in Hong Kong.

Add to that persistent job losses and reduced factory purchases, Qu said the data called for more stimulus measures to stoke domestic demand and economic growth.

HSBC/Markit said companies had reported a broad weakening in overseas demand last month, which reduced factory production and fueled job cuts among manufacturers.

The PMI showed factory employment shrank in May for the 18th straight month, even though the pace of contraction eased from the rates seen in March and April.

As the economy softened, deflationary pressure remained stubborn. The sub-indices for input and output prices were a good way under 50 points, though the rate of decline in input prices eased markedly.

China's economy has foundered this year as a cooling housing market and slowing growth in exports, domestic investment and consumption knocked growth to a six-year low of 7 percent in the first three months of the year.

Cooling inflationary pressure is especially problematic for China as it raises the real cost of borrowing for private firms, the biggest employers in the country but which are often denied of credit by banks.

Many analysts expect China's economy to grow 7 percent this year compared to 2014, the weakest rate in a quarter of a century and down from a 7.4 percent expansion last year.

That has fueled speculation that China's central bank, which has cut interest rates three times in six months, is likely to lower rates again this year.

Reporting by Koh Gui Qing;

Editing by Simon Cameron-Moore