(Recasts, adds quote, updates prices)

* ECB seen easing on Thursday, Canada may cut on Wednesday

* Treasury yields drop after surprisingly soft US ISM survey

* Oil drops after OPEC+ cuts, European gas prices surge on outage

June 3 (Reuters) - World stocks climbed on Monday while Treasury yields dropped after data showed unexpected weakness in U.S. manufacturing activity, adding to uncertainty around the prospect of U.S. interest rate cuts this year.

The cloudy outlook for U.S. rates contrasts with Europe, where investors are looking forward to a 25-basis-point interest rate cut by the European Central Bank on Thursday, which would bring the benchmark rate down to 3.75%.

By 1517 GMT, the MSCI All Country World Price Index rose 0.33%, although U.S. stock indices flipped into losses, amid a reported technical glitch on the New York Stock Exchange regarding "Limited Up-Limit Down" bands that sent dozen of stocks listed on the exchange into volatility pauses.

The exchange said it was investigating the problem and will provide information as soon as possible.

The S&P 500 index edged 0.1% lower, the Dow Jones Industrial Average shed 0.6% while the Nasdaq Composite lost 0.37%. In contrast, the pan-European STOXX index was up 0.33%

Benchmark U.S. Treasury yields fell to a two-week low after data showed that U.S. manufacturing activity slowed for a second straight month in May, as new goods orders dropped by the most in nearly two years.

The soft data supported some speculation that the Federal Reserve might cut interest rates this year, although some investors remained sceptical about the chance of rate cuts with inflation standing above its 2% target.

"We see inflation limiting how much central banks can cut interest rates," Jean Bolvin, the head of Blackrock Investment Institute, said. "We see them keeping rates high for longer."

Benchmark 10-year note yields were last down 9 basis points at 4.418%, and got as low as 4.404%, the lowest since May 21. Two-year note yields fell 7 basis points to 4.823% and reached 4.816%, also the lowest since May 21.

The inversion in the two-year, 10-year yield curve , a possible indicator of future economic downturn, deepened 3 basis points to minus 41 basis points.

In Europe, even though the ECB is considered almost certain to trim rates on Thursday, last week's surprisingly strong euro zone inflation data further weakened the case for a rapid round of reductions.

Markets now price in fewer than 60 basis points of easing - meaning two 25-basis-point cuts and less than a 50% chance of a third.

"There's a relatively positive risk tone to start the week, which seems like a continuation of the positive momentum seen on Friday, albeit is somewhat surprising given the bumper calendar of event risk coming up," said Michael Brown, strategist at broker Pepperstone in London.

China's factory activity grew at the fastest pace in about two years in May, data showed on Monday. That extended the optimism prevailing in markets following Friday figures showing the U.S. Federal Reserve's preferred measure of inflation held steady in April.

"The ECB decision is perhaps the most important event to watch, particularly after last week’s inflation data which raises the hawkish risk that there is only one more cut this year after a 25bp reduction on Thursday," Brown said.

Markets also imply around an 80% chance the Bank of Canada will cut rates at its meeting on Wednesday and around 60 basis points of easing this year, though analysts are hopeful the easing will be even deeper.

ASIAN STRENGTH

The dollar fell to a three-week low after the weak U.S. manufacturing data. The dollar index, a measure of the U.S. currency's value versus six major currencies, slipped 0.3% to 104.24. The index earlier dropped to a three-week low of 104.22.

The greenback also fell to a two-week low against the yen following the data and was last down 0.6% at 156.245.

The euro rose 0.4% against the dollar at $1.08893.

In other currencies, the Mexican peso weakened on Monday after the ruling party declared Claudia Sheinbaum the winner of the presidential election by a "large margin" after polls closed on Sunday. The U.S. dollar was last up 3.1% at 17.52 pesos .

India's rupee strengthened and its stock market rose to a record high, buoyed by expectations of sustained economic growth as Prime Minister Narendra Modi looked set for a third term.

Gold was up 0.7% at $2,342.9 an ounce, having now rallied for four months in a row, helped in part by buying from central banks and China.

Oil prices slumped 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. Some analysts described the group's decision, agreed on Sunday, as incrementally bearish for oil prices.

Brent tumbled 3.4% to $78.33 a barrel, while U.S. crude dropped 3.65% to $74.21 per barrel.

European natural gas prices rose more than 8% to their highest this year at over 37 euros/ MWh as an outage in Norway, which overtook Russia in 2022 as Europe's biggest gas supplier, pushed exports sharply lower on Monday. ($1 = 157.1900 yen)

(Reporting by Yoruk Bahceli and Wayne Cole; Editing by Jamie Freed, Christopher Cushing, Rashmi Aich, Alex Richardson, Susan Fenton and Andrew Heavens)