Both indexes use a 100-point scale on which numbers below 50 indicate contraction.
Domestic demand looks to be driving the improvement in manufacturing. HSBC's survey, which is tilted to small- and medium-sized private enterprises, found new export orders continued to decline because of sluggish demand in the U.S. and Europe. The federation's survey, meanwhile, gives an outsize representation to China's big state-owned enterprises, which hardly compete in export markets.
The signs of improvement in China's massive manufacturing industry will offer encouragement to China's leaders, who are trying to reverse a slowdown that's pulled economic growth to a two-decade low of 7.5 percent in the latest quarter.
"Growth in China's manufacturing sector has started to stabilize on the back of a modest rebound of new orders and output," said HSBC's chief China economist, Qu Hongbin. "This was mainly driven by the initial filtering through of recent stimulus measures and companies' restocking activities."
China's leaders say they're comfortable with slower growth as they try to steer the economy away from an export-driven model to one based on domestic consumption. They've opted for measures to bolster individual areas of the economy such as railways and small businesses rather than an across-the-board stimulus.
Analysts said the upbeat manufacturing reports ease pressure on policymakers to unleash more stimulus.
HSBC's survey, based on responses from 420 companies, confirms a preliminary version released last month.
Other recent signs of possible improvement in China's economy include a 10.9 percent surge in July imports that beat expectations, while exports grew 5.1 percent.