China Caixin services purchasing managers' index (PMI) on Wednesday showed growth slowed in June, as new order volumes weakened, but it continued to show rising demand.

The June Business Activity Index came in at 51.6, down from May's four-month high of 52.8, with the release from Caixin and PMI by IHS Markit saying it pointed to a further rise in service-sector activity.

Levels above 50 signal an expansion, while levels below 50 indicate contraction.

But while that signaled expansion, it was the second-weakest level in the past 13 months, the release said, noting that while some of the panelists surveyed said improved sales had boosted activity, others indicated subdued new order growth and difficulties securing loans weighed.

That was less enthusiastic than the official services PMI for June, released last week, which rose to 54.9 from May's 54.5.

The Caixin PMI tends to focus on smaller, private companies, while the official data tends to focus on larger, often state-owned companies.

The Australian dollar (Exchange: AUD=) edged higher after the release, rising as high as $0.7621 from around $0.7609 before the data. At 10:20 a.m. HK/SIN, the Aussie dollar was fetching $0.7617.

China is a key destination for Australia's exports of commodities.

Donna Kwok, senior China economist at UBS, told CNBC's " Squawk Box " that she wasn't worried about the services PMI decline.

She noted that as a sentiment indicator, PMI tends to fluctuate month-to-month, but it remained in a range "comfortably" over 50.

"For the second quarter, we've got a still solidly humming economy at play," she said, forecasting second-quarter economic growth at 6.8 percent.

In the first quarter, China's GDP grew 6.9 percent on-year, slightly faster than the 6.8 percent forecast in a Reuters poll and the fastest pace since the third quarter of 2015. The government was targeting growth of around 6.5 percent for this year

While the manufacturing PMI data tends to be more closely watched, China's pivot toward domestic consumption and away from investment-led growth means the services sector accounts for a bigger slice of the mainland economy. The services sector includes consumer industries such as real estate, retail and leisure.

The Caixin China Composite PMI, which includes both manufacturing and services, slipped to 51.1 in June, from May's 51.5, the slowest expansion in a year.

"Even though the impact of slowing expansion in China's services sector was cushioned by a slight rebound in manufacturing activity, the downward trend in the economy remains entrenched," Zhengsheng Zhong, director of macroeconomic analysis at CEBM Group, said in the Caixin PMI release.