A private survey of China's factory sector showed on Monday that manufacturing activity was slightly better than expected in May.

The Caixin/Markit factory Purchasing Managers' Index for May was 50.2. Analysts polled by Reuters had expected the indicator to come in at 50. The PMI reading for April was 50.2.

PMI readings above 50 indicate expansion, while those below that signal contraction.

Last week, China's official manufacturing PMI for May came in at 49.4, lower than the 49.9 economists polled by Reuters had forecast. It was lower than April's reading of 50.1. The official non-manufacturing PMI for May was 54.3 — unchanged from April.

Growth of new orders grew in May, and the rate of new business growth quickened slightly in the last month, Caixin said in a statement on Monday.

"The stronger rise in overall new business supported a renewed expansion in buying activity among Chinese manufacturing firms. Though only slight, it was the first time that purchasing activity had increased for five months," the statement added.

Despite the steady reading that was still in expansionary territory, business confidence slipped to the lowest level since the survey series began in April 2012.

That was "amid concerns of an escalating China-US trade war and forecasts of relatively subdued global demand," the satement added.

Analysts had warned that the official PMI data show that growth in China remains under pressure, despite earlier optimism that Chinese officials managed to stabilize the world's second-largest economy.

Before the release of the Caixin indicator, an economist from Mizuho Bank said the data "will not supplant the overall sense of economic pessimism" even if it turns out "unexpectedly resilient."

"Our best guess is that despondency will build up around China's growth/exports expectations, spilling over more widely to the rest of Asia/Australia, in the near-term," Vishnu Varathan, Mizuho's head of economics and strategy, wrote in a Monday morning note.

"What's more, the wider strategic tech war playing out with Huawei (and related suppliers and advanced Chinese tech companies) also creates a chill around the outlook for not only for exports, but for wider commercial activity as well," he added.

The PMI is a survey of businesses about the operating environment. Such data offer a first glimpse into what's happening in an economy, as they are usually among the first major economic indicators released each month.

For China, the PMI is among economic indicators that investors globally watch closely for signs of trouble amid domestic headwinds and the ongoing U.S.-China trade dispute.

The official PMI survey typically polls a large proportion of big businesses and state-owned enterprises. A separate survey, the Caixin indicator, features a bigger mix of small- and medium-sized firms.