* China factory activity improves but still contracts
* New export orders at 4-yr high but domestic demand weak
* Adds to signs of stabilisation in economy, headwinds linger
BEIJING, June 3 (Reuters) - China's factory sector turned in its best performance in four months in May as export orders improved although activity still contracted, a private survey showed on Tuesday, adding to signs the economy may be stabilising.
The final reading of the HSBC/Markit purchasing managers' index (PMI) for May rose to 49.4, lower than a preliminary reading of 49.7 but up from 48.1 in April.
The final PMI was weaker than the flash reading due to an upward revision of the stocks of finished goods, HSBC said.
The new export orders sub-index rose to four-year high of 53.2 in May from April's 48.9, but the new orders sub-index barely stopped contracting, suggesting domestic demand remains sluggish despite the improving global demand.
The HSBC/Markit PMI has been below the 50 level that separates growth from contraction since the start of 2014.
"The final PMI reading for May confirmed that the economy is stabilising, but it is too early to say that it has bottomed out, particularly in light of a weaker property sector," said Qu Hongbin, chief economist for China at HSBC.
"The lack of a sustainable growth momentum warrants stronger policy support. We expect both monetary and fiscal policy to be loosened gradually over the coming months."
The official PMI hit a five-month high of 50.8 in May from April's 50.4, the National Bureau of Statistics said on Sunday, beating market expectations of 50.6.
The official PMI is weighted more towards bigger and state-owned enterprises and tends to paint a rosier picture than the HSBC/Markit survey, which focuses more on smaller private firms.
The HSBC/Markit survey also pointed to weaker employment in the manufacturing sector in May. China has attributed its relatively stable jobs market to the services sector.
The government has unveiled a slew of targeted policy measures, including faster investment in railways and public housing, in recent weeks to underpin the slowing economy.
Last week, China's cabinet announced fresh supportive measures, including cutting reserve requirement ratios (RRR) for more commercial banks, expanding re-lending and bond financing to support small firms.
The central bank has already cut RRR for rural banks.
On the fiscal front, the finance ministry has urged local governments and state agencies to quicken budget spending.
Chinese leaders have ruled out the possibility of any big fiscal stimulus as they focus on reforms to try to put the economy on a more sustainable footing over the long term.
The world's second-largest economy faces headwinds from a downturn in the property sector, which would spill-over into wide-range of industries, analysts say.
A Reuters poll shows analysts expect annual GDP growth to slow to 7.3 percent in the second quarter from an 18-month low of 7.4 percent in the first quarter. They expect full-year growth of 7.3 percent in 2014, the weakest in 24 years. (Reporting by Kevin Yao; Editing by Kim Coghill)