(Reuters) -Asia's big manufacturing hubs struggled to fire up in October, business surveys showed on Monday, as weak U.S. demand and tariffs under President Donald Trump hit factory orders across the region.

While Trump's visit to Asia last week led to some progress in trade negotiations with large manufacturing economies such as China and South Korea, exporters continue to be cautious about U.S. demand.

Private-sector purchasing managers' indexes (PMIs) for October released on Monday showed manufacturing activity growing at a slower pace in China and falling in South Korea, with export orders in both countries declining.

Friday's official PMI survey showed China's factory activity falling for the seventh straight month, confirming suspicions that the earlier export rush to get ahead of U.S. tariffs had well and truly ended.

"The PMIs suggest that China's economy lost some momentum in October, with slower growth across manufacturing and construction," said Zichun Huang, China economist at Capital Economics. "Some of this weakness may reverse in the near term, but any boost to exports from the latest U.S.-China trade 'deal' is likely to be modest and wider headwinds to growth will persist."

CAUTIOUS OPTIMISM ON TARIFFS PROGRESS

In a meeting in South Korea last week, Trump and Chinese President Xi Jinping agreed to de-escalate tensions, including through a one-year delay in reciprocal tariffs, but the agreement does little to address a deeper divide between the two superpowers.

Policymakers in Beijing are looking to see whether China's $19 trillion economy is on track to hit its official 2025 growth target of around 5%, without needing to reach for further stimulus.

Trade data for September showed China's exports rising faster-than-expected, although this was mostly due to growth in new markets as U.S.-bound shipments tumbled 27% year-on-year.

Similarly, Seoul's trade deal with Trump announced last week secured lower U.S. tariffs on Korean goods, but was seen at best as a compromise that prevents Asia's fourth-largest economy from falling behind in global trade.

Elsewhere in Asia, continued declines were also seen in factory activity in Malaysia and Taiwan, PMIs showed, although Vietnam and Indonesia saw growth in their manufacturing sectors pick up.

(Reporting by Asia Newsrooms; Writing by Sam Holmes; Editing by Jacqueline wong)