LONDON, Sept 5 (Reuters) - Global equities were lower on Tuesday as weak service sector data from China and Europe rekindled worries over the global economy, while Australia's central bank kept interest rates unchanged, pushing the Australian dollar lower.

A private-sector survey showed on Tuesday that China's services activity expanded at the slowest pace in eight months in August as weak demand continued to dog the world's second-largest economy.

Data from the euro area and Britain also showed a decline in business activity in August, with the dominant services industry in both regions falling into contraction.

European equity indexes were mixed, with the pan-European benchmark STOXX 600 little changed.

Germany's DAX and France's CAC 40 were down 0.1% and 0.2%, respectively, while Britain's FTSE 100 eked out a 0.1% gain.

This followed a weak performance in Asia, where MSCI's broadest index of Asia-Pacific shares outside Japan fell 1.1%, moving away from a three-week high it touched on Monday.

That saw MSCI's gauge of stocks across the globe down 0.2%, while futures on Wall Street were signalling a negative open.

"The miss in China's Caixin services PMI has offset some of the sentiment shift we got yesterday," said Charu Chanana, market strategist at Saxo in Singapore.

Still, investors are hoping that Beijing's drip feed of policy stimulus will be enough to stabilise the Chinese economy.

"It feels like China has been tinkering around the edges and they probably need to do something more substantial," said Dan Boardman-Weston, CEO and CIO at BRI Wealth Management.

"They clearly want to sort out the property sector and make sure moral hazard doesn't encroach into the system, but I have been surprised by how seemingly weak the policy easing has been thus far."

The disappointing global data gave the U.S. dollar a lift, while its Australian counterpart shed over 1.5%, dropping to its lowest level since November at $0.6364 after the country's central bank held rates at 4.10% and said recent data were consistent with inflation returning to the 2% to 3% target range in late 2025.

"The key final paragraph was essentially unchanged, with a hawkish bias intact, but clearly no desire to act upon this bias unless forced by the data to do so," RBC capital markets chief economist Su-Lin Ong said in a note.

The Aussie also functions as a liquid proxy for the yuan , owing to the country's exports to China.

Meanwhile, the euro dropped 0.6% to $1.0729, a three-month low, and the Japanese yen weakened 0.5% to 147.33 per dollar, at levels that led to intervention from Japanese authorities last year.

This pushed the dollar index, which measures the U.S. currency against six rivals, to its highest since March at 104.75.

U.S. markets were closed on Monday for a holiday, leading to light trading volumes. While the economic calendar in the region is bare, several Federal Reserve officials are due to speak during the week.

Data on Friday showed U.S. job growth picked up in August, but the unemployment rate jumped to 3.8%, while wage gains moderated. The slight cracks in the labour market bolstered expectations that the Fed is likely done hiking rates.

Markets are pricing in a 93% chance of the Fed keeping rates unchanged later this month, according to LSEG data.

Markets are also now leaning against a hike at the European Central Bank's September meeting after a run of soft data.

In commodities, U.S. crude fell 0.3% to $85.27 per barrel and Brent was at $88.36, down 0.7% on the day, although both remain in close proximity to year-to-date highs.

"It'll be interesting to see how rising oil prices start to shape the inflation narrative again," BRI's Boardman-Weston said.

"If inflation starts accelerating again, the Fed might need to go higher than we thought," Boardman-Weston added.

(Reporting by Samuel Indyk and Ankur Banerjee; Editing by Stephen Coates, Kim Coghill, Christina Fincher and Shounak Dasgupta)