* Asian stock markets : https://tmsnrt.rs/2zpUAr4
* Nikkei extends bounce, US stock futures edge up
* ECB seen easing on Thurs, Canada may cut on Wed
* Focus on US ISM surveys, May payrolls reports
* Oil prices dip as OPEC+ extends most output cuts
SYDNEY, June 3 (Reuters) - Asian share markets rose on Monday as investors looked forward to a rate cut in Europe, and quite possibly Canada, as the next step in global policy easing, though sticky inflation threatens to make the process a drawn out affair.
The European Central Bank (ECB) is considered almost certain to trim rates by a quarter point to 3.75% on Thursday, the first time in history it would have eased ahead of the U.S. Federal Reserve.
However, a surprisingly high reading for Euro zone inflation out last week blunted hopes for a rapid round of reductions and markets have 55 basis points of easing priced in for this year.
"The probability of back-to-back cuts now appears very low, putting the focus for a second move on September," said Bruce Kasman, head of economic research at JPMorgan.
"We suspect President Christine Lagarde will signal that the direction of rates is downward next week, but the policy statement will emphasize that future moves are data-dependent, and there is no pre-commitment to a particular rate path."
Markets also imply around an 80% chance the Bank of Canada will cut at its meeting on Wednesday and 59 basis points of easing this year, though analysts are hopeful the easing will be even deeper.
Investors are a lot less dovish on the Fed, seeing little prospect of a move until September and even that is far from a done deal.
The outlook could change this week given data due includes key surveys on services and manufacturing, and the May payrolls report where unemployment is seen holding at 3.9% as 190,000 net new jobs are created.
The prospect of lower borrowing costs globally has been generally positive for equities, though disappointing economic news from China somewhat soured the mood in Asia.
MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.3%, having slid 2.5% last week.
Japan's Nikkei rose a further 1.0%, after rebounding from one-month lows on Friday.
Indian markets are waiting to see if Prime Minister Narendra Modi will expand his alliance's majority in parliament when election results are released on Tuesday, amid speculation this would lead to more economic reforms.
Month-end flows saw Wall Street stage a late rally on Friday and left the Nasdaq up almost 7% for May. Early on Monday, S&P 500 futures were up 0.2%, with Nasdaq futures adding 0.1%.
In forex markets, the Japanese yen remains the weakest of the majors, though the government is clearly prepared to spend big to slow its slide. Data out last week showed Tokyo spent 9.788 trillion yen ($62.27 billion) on currency intervention between April 26 and May 29.
The dollar stood at 157.15 yen, just off last week's peak of 157.715. The euro held firm at $1.0852, still benefiting from the EU inflation report, but faces resistance at $1.0895.
Gold was steady at $2,326 an ounce, having now rallied for four months in a row helped in part by buying from central banks and China.
Oil prices initially eased after OPEC+ agreed on Sunday to extend most of its oil output cuts into 2025, though some cuts will start to be unwound from October 2024 onwards.
Brent dipped 26 cents to $80.85 a barrel, while U.S. crude fell 22 cents to $76.77 per barrel. ($1 = 157.1900 yen)
(Reporting by Wayne Cole; Editing by Jamie Freed)
