LONDON, June 4 (Reuters) -

Stocks and commodities slid on Tuesday, as investors grew increasingly uneasy about evidence that the U.S. economy's "exceptionalism" may be starting to unwind as manufacturing activity there weakened further.

Several measures of volatility picked up, reflecting a degree of nervousness among traders, while classic safe-haven assets like bonds and the dollar itself remained in positive territory.

Oil, copper and gold also fell in the face of the stronger U.S. currency.

Earlier in the day, the dollar touched its lowest in over two months against the euro and the pound, while U.S. government bond yields have retreated over the past six weeks, as investors have bought into the idea that the economy is slowing enough to warrant rate cuts this year.

"It is understandable why the market behaved as it did in the first quarter, but if one looked at broader indicators, there have always been certain signs that maybe the story isn't quite as strong as might have been expected," Daiwa Capital economist Chris Scicluna said.

"Most people would have assumed that where the fed funds rate is right now is in restrictive territory. That is bearing down on underlying inflation and bearing down on some of the dynamism in spending," he said.

The MSCI All-World index was last down 0.3%. Stocks in Europe slid, led by energy, mining and banking stocks, pushing the STOXX 600 down by as much as 0.9%.

Losses accelerated in U.S. stock futures , which fell 0.5-0.6%, while Wall Street's so-called "fear index," the VIX rose by the most in a week, echoing a sharp rise in the Euro STOXX volatility index to a one-month high.

In India, share markets sold off sharply after early vote counting showed Prime Minister Narendra Modi's Bharatiya Janata Party (BJP)-led alliance was not headed for a landslide win as predicted.

A Modi victory had been expected to be positive for the country's financial markets, according to analysts, on the hope India will undertake further economic reform.

The reduced prospect of Modi's alliance winning an overwhelming majority rattled investors.

The Nifty index dropped as much as 8.6% before recovering some of those losses, while the BSE index dropped almost 6%. Both indexes had touched all-time highs on Monday.

Political jitters also knocked the Mexican peso and South Africa's rand, which dropped by 2.3% and 1.1%, respectively, following election results in both those countries.

JOBS, JOBS, JOBS

This week brings a slew of major data. The strength of the U.S. labor market will be closely watched in the new few days with the Job Openings and Labor Turnover Survey (JOLTS) due to be published later on Tuesday. Non-farm payroll figures for May are out on Friday.

"We're expecting a slight easing in demand for labor in the U.S. market," said Raisah Rasid, JPMorgan Asset Management's global market strategist.

"What does that mean for the Fed? I think all data points to one interest rate cut later in the year, potentially in December. If the data moves quicker than expected that cut could be moved forward to September."

On Monday, U.S. Treasury yields fell to the lowest point in two weeks, after the country's manufacturing activity slipped for the second consecutive month in May.

The yield on benchmark 10-year Treasury notes fell 2 basis points to 4.381%, while the two-year yield , which rises with traders' expectations of higher Fed fund rates, fell 1 bps to 4.8058%.

"The sharper move at the long-end is a sign that weaker manufacturing data is unlikely to shift the dial on Fed rate cuts near term, but is perhaps a signal of the market's view of neutral interest rates as US economic exceptionalism fades," Westpac economist Jameson Coombs said in a note on Tuesday.

In Europe, investors expect the European Central Bank on Thursday to cut the benchmark rate by 25 basis points to 3.75%.

The dollar fell 0.8% against the yen, viewed by many as a safe-haven asset because of the low interest rate it bears, to 154.88, around its lowest for two weeks and over 3% down from late April's multi-year high at 160.03.

The euro fell 0.3% to $1.0865, while sterling was at $1.0881, having gained 0.65% in a month, while the dollar index, which tracks the greenback against a basket of currencies of other major trading partners, rose 0.2% on the day to 104.28.

U.S. crude fell 2% to $72.73 a barrel. Brent crude fell 1.7% to $77. Both benchmarks hit four-month lows on Monday after the Organization of the Petroleum Exporting Countries and allies, together known as OPEC+, agreed to start unwinding some production cuts from October.

Gold dropped 0.9% to $2,330 an ounce, while copper, which hit record-highs last month, fell 1.6% to $9,979 a tonne.

(Additional reporting by Scott Murdoch in Sydney; Editing by Sonali Paul, Philippa Fletcher and Chizu Nomiyama)