Updates at 0835 GMT

By Yoruk Bahceli and Tom Westbrook

Sept 3 (Reuters) -World stocks steadied on Tuesday and the dollar remained near a two-week high as investors turned cautious awaitinga raft of economic data thatmay determine how deeply the U.S. will cut interest rates.

Focus was on theU.S. ISM manufacturing activity surveydue later in the day, setting the scene ahead ofjobs data due on Friday that willbe crucial for whether the Federal Reserve cuts by 25 basis points or 50 on Sept. 18 and how much it delivers for the rest of the year.

World shares were steady, just a touch below record highs .MIWD00000PUS. Europe's STOXX 600 .STOXX U.S. stock futures ESc1, NQc1 were down 0.1-0.3%.

Ten-year Treasury yields were down a basis point to 3.90% US10YT=RR as trade resumed in Asia following a U.S. holiday.

Economists forecast the ISM survey improving but remaining in contractionary territory at 47.5 in August.

"We think market reaction to any surprise will likely be contained today given the event risk ahead of us," said Evelyne Gomez-Liechti, rates strategist at Mizuho in London.

On Friday, analysts are looking for a rise of 160,000 in U.S. non-farm payrolls (NFP) and a dip in the unemployment rate to 4.2%.

July's jobs data, which showed the unemployment rate jumped near a three-year high of 4.3% amid a significant slowdown in hiring. The data, along with a wind-down of yen carry trades, rocked global markets and investors have doubled the rate cuts they expect from the U.S. Federal Reserve this year.

Traders now price in around 100 basis points of Fed cuts this year across three meetings, meaning they foresee a big 50 bps cut at one of them FEDWATCH.

But many investors say that is overpriced given a relatively healthy U.S. economy.

Stock markets have recovered from their early August rout, while bond markets continue to hold onto gains, painting a puzzling picture.

"It really boils down to Friday's number," said Raisah Rasid, global market strategist at J.P. Morgan Asset Management in Singapore, with policymakers looking for a cooling labour market to clear the way for rate cuts.

"We don't see any stress or indications that would necessitate a 50 basis point cut ... the question is how long will risk assets continue to rally?"

The dollar =USD held near a two-week high on Tuesday against a basket of currencies.

The euro EUR=EBS was down 0.2% against the dollar, but held above a two-week low it hit on Monday.

"If NFP comes in on target, or close toit, that's probably going to lock in that 25-bps cut and I think because of that we'll probably see some more dollar appreciation," said Nick Twidale, chief market analyst at ATFX Global in Sydney.

YEN STRENGTH

Japan's yen JPY=EBS, meanwhile, was up 0.8% against the U.S. dollar to 145.735.

It broke a four-day losing streak with media reports citing the Bank of Japan governor reiterating that the central bank would keep raising interest rates if the economy and inflation performed as policymakers currently expect.

Earlier in Asia, MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS ticked 0.5% lower as fallingprofits weighed on China's banking sector .SS, while Japan's Nikkei .N225 fell 0.3%%

Brent crude futures LCOc1 dropped for a third straight session and were last down 0.9% to $76.84 a barrel.

Oil prices rose over $81 in late August as political tensions in Libya led to a halt in exports, but have struggled for traction since as demand worries have weighed.

Gold XAU= edged higher around $2,505 an ounce after hitting a record high of $2,531 inAugust.

Reporting by Yoruk Bahceli and Tom Westbrook; Editing by Shri Navaratnam, Kim Coghill and Toby Chopra

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