GLOBAL MARKETS-Oil tumbles on demand worries; stocks hit by trade and economic fears

By Sinéad Carew

* Stock indexes around the world fall on economic/trade jitters

* Investors weigh U.S. data and ongoing trade tensions

* Hopes high for Fed rate cut hints ahead of June meeting (Updates to late afternoon, adds commentary)

By Sinéad Carew

NEW YORK, June 12 (Reuters) - Oil futures sank 4% on Wednesday amid higher U.S. crude inventories and a bleaker demand outlook, while uncertainty over the U.S.-China trade war and U.S. economic data weighed on stocks.

The dollar index rose as trade tensions and U.S. interest rate policy remained in focus after President Donald Trump expressed optimism over making a trade deal with China.

Earlier in the day, May data showed moderate inflation as U.S. consumer prices barely rose. That, with a slowing economy, could build a case for the Federal Reserve to cut interest rates.

"Typically the market would read that as being a negative for the economy," said Matt Watson, associate director of research at James Investment Research in Alpha, Ohio.

Investors were hoping the U.S. Federal Reserve would give hints about a rate cut after its June 18-19 meeting.

And after a five-day rally, Watson said: "we're seeing a little bit of profit taking prior to investors going into a wait and see mode before the Fed meeting next week to see if they're going to lower interest rates or not."

While market participants eyed the latest data as potential support for a rate cut, it was not enough to outweigh worries about the economic impact of escalating trade tensions.

With under three weeks to go before proposed talks between U.S. President Donald Trump and Chinese President Xi Jinping at the June 28-29 G20 summit in Osaka, Trump said on Wednesday that he had a "feeling" a U.S.-China trade deal could be reached. But he again threatened to increase tariffs on Chinese goods if there is no agreement.

The Dow Jones Industrial Average fell 58.02 points, or 0.22%, to 25,990.49, the S&P 500 lost 6.77 points, or 0.23%, to 2,878.95 and the Nasdaq Composite dropped 32.40 points, or 0.41%, to 7,790.17.

The pan-European STOXX 600 index lost 0.30% and MSCI's gauge of stocks across the globe shed 0.39%.

OIL FALLS, TREASURY YIELD CURVE STEEPENS The U.S. Treasury yield curve was steeper after soft inflation data pulled short-dated yields lower, indicating increased expectations the Federal Reserve will cut interest rates.

Looking ahead, "focus will continue to turn to headlines surrounding trade. Also in focus the remainder of the week will be the $16 billion 30-year auction tomorrow (Thursday) and retail sales on Friday," wrote Justin Lederer, Treasury analyst and trader at Cantor Fitzgerald.

Benchmark 10-year notes last rose 5/32 in price to yield 2.1239%, from 2.14% late on Tuesday.

In currency markets, the dollar index, tracking the currency against six major peers, rose 0.32%, with the euro down 0.4% to $1.1284.

The euro dropped as Trump said he was considering sanctions over Russia's Nord Stream 2 natural gas pipeline project and warned Germany against being dependent on Russia for energy.

Oil prices extended their losses as the day wore on, weakened by an unexpected rise in U.S. crude inventories and by a dimming outlook for global oil demand.

"The fact that this surplus has been mounting during the past couple of months despite a near record pace of exports in recent weeks is not only suggesting weak demand from the refiners but also a much stronger pace of imports than we had anticipated," Jim Ritterbusch of Ritterbusch and Associates said in a note.

U.S. crude was down 4.0% at $51.14 per barrel while Brent crude futures settled down 3.7% or $2.32 at $59.97.

(Additional reporting by Laila Kearney, Kate Duguid, Karen Brettell and Caroline Valetkevitch in New York; Editing by Bernadette Baum and Chizu Nomiyama)