SINGAPORE (Reuters) - Asia's factories showed few signs of returning to health in August, as torpid activity in the region's biggest economies, China and Japan, suggested world demand remained fitful at best even as global policymakers scrambled to restore momentum.

Coming a week after the United States posted sluggish second quarter growth, Asia's uninspiring manufacturing surveys may give Federal Reserve Chair Janet Yellen pause for thought ahead of a Fed meeting on Sept. 20-21 to decide whether or not to raise interest rates.

Moreover, the still-unknown impact of Britain's shock decision in June to quit the European Union is seen chilling already soft consumption, leaving factories struggling to clear their goods.

In China, the world's second-biggest economy, factory activity showed scant growth.

The official Purchasing Managers' Index (PMI) ticked up to 50.4 in August, compared with the previous month's 49.9 and just above the 50-point mark that separates growth from contraction. But the private Caixin version of the PMI, which covers a greater share of smaller firms, showed activity stagnated last month with the index at 50.0, from an unexpectedly upbeat 50.6 in July.

"Downward pressure on China’s economy remains and government support to stabilize growth must continue," Zhengsheng Zhong, director of macroeconomic analysis at CEBM Group, said in a note accompanying the Caixin PMI report.

Indeed, with central banks almost exhausting their monetary policy support, governments in Asia have increased fiscal stimulus although underlying demand in many of the region's export-reliant economies remain weak.

"A still subdued external demand environment and fading policy pass-throughs is weighing on aggregate demand in the region," said Chetan Ahya, senior economist at Morgan Stanley. "In the near-term, the growth trajectory will depend on the trend in external demand, and monetary and fiscal policy response."

WEAK EXPORTS HIT JAPAN, S.KOREA

In Japan, while manufacturing activity showed signs of steadying, the IHS Markit/Nikkei PMI was still in contraction at 49.5 in August versus 49.3 in July.

Export orders continued to fall, even as output increased for the first time in six months, backing expectations the Bank of Japan will need to offer more stimulus on top up its already massive easings to revive a sputtering economy.

The pressure on Japanese policy makers was underscored by separate data showing Japanese business expenditure fell in April-June from the previous quarter.

Conditions were even more gloomy in South Korea, a bellwether for global demand. An extended slide in exports put manufacturers in Asia's fourth largest economy to the sword, with the August PMI contracting at its fastest pace in a year.

Other data showing Korean exports rebounded last month was seen as an aberration due to two extra working days this year.

"Given Korea acts as a harbinger for the rest of Asia, we believe Asia’s cycle is now headed for another down-move," said Vaninder Singh, Asia economist at RBS in a note to clients.

The situation in Malaysia was no better, with manufacturing activity in August contracting at a quicker rate than in July, although Taiwan was a surprising outlier with activity there expanding at the fastest pace in 1-1/2-years.

Still, broad-based weakness in external demand called for further policy support, including interest rate cuts, analysts said.

"We won’t rule out rate cuts in Malaysia or Korea, and expect further monetary policy easing in Indonesia, Taiwan and Thailand this year," said Krystal Tan, Asia economist at Capital Economics.

There were some encouraging signs in India where August factory activity expanded at its fastest pace in 13 months, but investors will have to square that with data released on Wednesday that showed economic growth slipped to over a one-year low between April and June.

Surveys from Europe and the U.S. are due later Thursday, and while data has indicated pockets of strength the overall picture is one of slow growth, especially in the eurozone where worries remain over fallout from Brexit.

On Wednesday, the Institute for Supply Management-Chicago said its business barometer dropped 4.3 points to 51.5 in August, falling short of expectations.

While the focus will move to the key August U.S. jobs data due on Friday, struggling global manufacturers should give the Fed pause as it considers the next rate hike.

(Corrects milestone for India PMI to highest in 13 months, not 15 months, in 18th paragraph)

(Reporting by Yawen Chen & Sue-Lin Wong in Beijing, Minami Funakoshi in Tokyo, Cynthia Kim in Seoul, Karen Lema in Manila and J.R. Wu in Taipei; Writing by Shri Navaratnam; Editing by SImon Cameron-Moore)