(Updates prices)

* World shares, dollar gain

* ECB policy meeting on Thursday

* Canada cuts rates by 25 bps for first time in 4 years

* India stocks bounce after vote selloff

* Muted US private payrolls data bolster rate cut bets

NEW YORK/MILAN, June 5 (Reuters) - World shares rose and Treasury yields fell on Wednesday as investors focused on an upcoming European Central Bank policy meeting following soft U.S. labour market data that firmed up bets of a September Federal Reserve interest rate cut.

Investor hopes that lower interest rates -- which can be a boon for stock markets -- are in the offing were further bolstered after Canada's central bank cut interest rates by 25 basis points for the first time in four years.

Combined with yet another muted U.S. labour report that showed private payrolls increased by 152,000 jobs last month, less than forecast, some analysts predicted that the Federal Reserve could be on track to start lowering rates this year.

"The labor market should not be seen as a risk for inflation any longer," analysts at TD Securities said. "It is also supportive of the Fed beginning to ease policy in September if inflation continues to gradually normalize as we expect by then."

The MSCI world equity index, which tracks shares in 49 countries, was up 0.7% by 1731 GMT, supported by gains in Asia, Europe and on Wall Street. The S&P 500 index jumped 0.9%, the Dow Jones Industrial Average was flat and the Nasdaq Composite Index climbed 1.6%.

The ECB meets on Thursday, and money markets price in an almost certain chance of a first interest rate cut. However, there is uncertainty about the future path of euro zone rates.

"I have a positive view on tomorrow's cut because it marks the end of an era of rate hikes that began two years ago," said Carlo Franchini, head of institutional clients at Banca Ifigest.

"Now, we'll need to see the impact that rate cuts will have on domestic demand and the economic recovery".

Data on Wednesday showed euro zone business activity expanded at its quickest rate in a year in May as growth in the services industry outpaced a contraction in manufacturing.

The pan-European STOXX 600 index was up 0.8% and the MSCI's broadest index of Asia-Pacific shares outside Japan rose 1%. The Nikkei in Tokyo fell 0.9% as renewed strength in the Japanese yen weighed.

Data on Tuesday showed U.S. job openings fell more than expected in April to the lowest in more than three years, a sign that labour market conditions are softening.

The data emboldened bets on Fed rate cuts this year, with markets pricing in 45 basis points of easing, helping Wall Street end up just slightly on Tuesday.

Traders are pricing in a 65% chance of a rate cut in September, compared with 46% a week earlier, the CME FedWatch tool showed.

"Economic data in America are frankly weakening. In the past, such data caused a robust repricing and then nice rallies in the stock market. Now, this is somewhat less so," said Giuseppe Sersale, portfolio manager at Anthilia.

"The market seems to be shifting from a phase where it celebrated bad data to being a little afraid that the slowdown will be a little more pronounced. This explains why stocks have been moving sideways for several weeks now," he added.

Services ISM data for May due later on Wednesday will be watched for more indications about the U.S. economy ahead of the crucial payrolls report on Friday.

In keeping with expectations of lower U.S. rates, benchmark 10-year Treasury yields fell to 4.3007%, the lowest in more than two months.

Germany's 10-year government bond yield, the benchmark for the euro zone, nudged lower to 2.527% after its sharpest two-day drop since March in the previous session.

The dollar index, which measures the U.S. currency against six peers, was 0.25% higher at 104.42, just above the near two-month low of 103.99 it hit on Tuesday.

The dollar's relentless strength in the recent past will make way for minor weakness over the next 12 months, according to a Reuters poll of strategists who generally agreed the dollar was overvalued.

The U.S. currency's retreat helped the yen strengthen to a more than two-week high of 154.55 per dollar on Tuesday. On Wednesday, it weakened to 156.21.

In Asia, Indian markets stayed in focus, with stocks rising after Tuesday's plunge as voting results showed a slimmer-than-expected victory margin for PM Narendra Modi.

India's Nifty 50 rose 3.4% in volatile trading after sliding nearly 6% on Tuesday, its worst session in four years, with foreign investors selling roughly $1.5 billion of shares.

Modi's ruling Bharatiya Janata Party lost an outright majority in parliament for the first time in a decade and is dependent on its regional allies to get past the half-way mark required to run the world's largest democracy.

In commodities, oil prices were above four-month lows as traders weighed an OPEC+ decision to boost supply later this year and an increase in U.S. crude and fuel stockpiles.

Brent crude futures were last at 78.42 per barrel, up 1.2%, while U.S. West Texas Intermediate crude futures traded at $74.2 a barrel, also up 1.3%.

(Reporting by Danilo Masoni in Milan and Ankur Banerjee in Singapore; Editing by Marguerita Choy and Alexander Smith)