 "China's factories struggle for growth in lacklustre Asia")
Similar purchasing managers indexes measuring the factory sectors in India, South Korea and Taiwan rose modestly, although the improvements were not enough to give much comfort.
The one bright spot for Asia was in Japan, where a report said on Monday that manufacturing activity expanded in September at its fastest pace since the 2011 earthquake and tsunami.
China's official PMI rose to 51.1 in September from 51.0 in August, data showed on Tuesday. That was still the highest in 17 months, but the increase was less than expected.
A separate China PMI from HSBC on Monday also showed manufacturing activity growing less than expected last month on soft domestic demand.
"The question is how sustainable is the recovery," said Haibin Zhu, chief China economist for JP Morgan in Hong Kong.
"We are still cautious. We see the recovery peaking in Q3 and slowing in Q4 on a sequential basis."
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China's economy has shown signs of picking up but the PMI figures suggest it is struggling for momentum. Analysts like Zhu have warned China's economic rebound could be short-lived. Unlike in the past, the government is reluctant to implement strong stimulus policies that could come back to haunt it longer term.
The government PMI is more weighted towards larger, state-owned companies than the HSBC version, which focuses more on smaller and private-sector firms.
China's struggle adds to a complicated global economic environment for policy makers and investors. The US government began a partial shutdown on Tuesday for the first time in 17 years after lawmakers could not break a political stalemate over spending. It faces another critical deadline in coming weeks to raise its debt ceiling of $16.7 trillion. Failure to find an agreement could lead to a historic US government debt default.
A government crisis in Italy is presenting fresh stumbling blocks to a nascent recovery in the euro zone economy.
The euro zone and the United States are set to report manufacturing activity data later in the day.
FOCUS ON POLICY MAKERS
China's government is seen as unlikely to do much to support economic growth beyond mild measures it has announced so far, including accelerating infrastructure investment, mindful of the lessons learned in 2009 when a massive stimulus package saddled the country with massive debt that remains today.
China's government has set a 7.5% growth target for the economy in 2013, a goal officials expected to meet, but which would still mark the weakest expansion in 23 years.
Manufacturing surveys in South Korea and India on Tuesday showed activity contracted less sharply last month than in August, while Taiwan saw sector-activity growth pick up.
"The stronger PMI shows that Korea's manufacturing sector remains on track for a recovery towards year end," HSBC economist Ronald Man said in a statement. "But the pickup will be gradual because new orders received, especially on the external front, are still in contraction territory."
Indonesia's factory sector activity picked up in September but new orders and export orders fell. However, other data showed the country produced a trade surplus of $130 million in August, a sharp turnaround from a deficit of $2.3 billion in July and confounding expectations for a deficit of $890 million, while consumer prices rose much less sharply in September.
While there are fresh concerns about the United States and the euro zone, policy makers in emerging economies face issues of their own. India and Indonesia are suffering a loss of investors confidence over their current account deficits as markets anticipate a tapering of US monetary stimulus in coming months.
Indonesia will announce a second fiscal stimulus package this month as part of efforts to cut its ballooning current account deficit, the Jakarta Globe daily quoted a senior government official as saying on Tuesday.
Meanwhile, India's current account gap in the three months through June widened to 4.9% of gross domestic product from 3.6% in the previous quarter, while the fiscal deficit widened sharply in the first five months of the fiscal year, data showed on Monday.