BEIJING (Reuters) - China's factory activity likely grew for the fourth month June but the pace may be waning, as global demand stayed subdued while a fresh coronavirus outbreak in the Chinese capital and rising worldwide cases threaten to undermine a gradual domestic recovery.

The official manufacturing Purchasing Manager's Index (PMI), due for release on Tuesday, is expected to ease to 50.4 in June, from 50.6 in May, according to the median forecast of 29 economists polled by Reuters. A reading above 50 indicates an expansion in activity.

With travel bans finally lifted in April in Wuhan, the epicentre of the country's coronavirus crisis, China has largely managed to recover from strict lockdowns that had led to weeks of economic paralysis.

Yet export demand has remained weak with infections steadily rising across the world. Some fear a worldwide recession might turn out to be more pronounced than expected in the event a second wave of coronavirus cases force many countries to reimpose strict lockdowns.

Earlier this month a cluster that has steadily grown to more than 200 cases associated with a food market emerged in Beijing, underscoring the ever present economic threat posed by the virus.

"We received a stark reminder this week that the fight against COVID-19 is not over, as new cases globally thrice reached new highs," Morgan Stanley said in a note Monday.

'NOT MUCH ROOM'

The fallout from the global pandemic has left factories in China, and elsewhere, operating below strength amid slack demand.

"China's work resumption has become stable. There is not so much room (for a rebound) compared to the previous months," said Hu Yanhong, a researcher at Yingda Securities.

In May, China's exports beat expectations with a 3.3% fall thanks to pandemic-related medical supply demand. However, Capital Economics noted this boost is "unlikely to last as the transition to working-from-home reverses and stockpiling of masks and other protective equipment slows".

Underscoring persistent pressure on the manufacturing sector, China's producer prices fell by the sharpest rate in more than four years in May.

Beijing has announced a range of measures to bolster the economy and support jobs. The state cabinet this month flagged plans to further use monetary tools such as bank reserve ratio (RRR) cuts and relending to help firms secure cheaper loans.

The private-sector Caixin/Markit Manufacturing PMI, which analysts say focuses more on smaller export-driven firms, is expected to have also eased in June, slowing to 50.5 from the previous month's 50.7. The private PMI survey is due on Wednesday.

(Reporting by Yawen Chen and Ryan Woo; Editing by Shri Navaratnam)