* Stock indexes around the world dip with oil futures
* Investors weigh U.S. data and ongoing trade tensions
* Hong Kong markets, exposed shares hit by local unrest (Updates after U.S. market open, adds commentary, changes byline, previous dateline LONDON)
By Sinéad Carew
NEW YORK, June 12 (Reuters) - Oil futures sank on Wednesday amid higher U.S. crude inventories and a weaker demand outlook, while uncertainty over the U.S.-China trade war and its potential economic impact weighed on stock markets.
The dollar index was barely higher after 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.
"I don't think this signals an inflation slump or anything. But, it's still going to fuel expectations of ease," said Michael Cloherty, head of U.S. rates strategy at RBC Capital Markets.
While stock market participants also eyed the latest data as a potential support for a rate cut, that 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, expectations for progress toward ending the trade war were low here and sources told Reuters that there had been little preparation for a meeting.
"This is a market that would love to see us get back to the negotiating table. The longer these trade tensions last, the most damage it'll do to the economy, and therefore to earnings," said Art Hogan, chief market strategist at National Securities in New York.
The Dow Jones Industrial Average fell 35.57 points, or 0.14%, to 26,012.94, the S&P 500 lost 5.12 points, or 0.18%, to 2,880.6 and the Nasdaq Composite dropped 30.56 points, or 0.39%, to 7,792.00.
The pan-European STOXX 600 index lost 0.25% and MSCI's gauge of stocks across the globe shed 0.25%.
Hong Kong's Hang Seng index sank 1.7% as tens of thousands of protesters stormed roads here next to government offices to protest against a bill that would allow China to extradite people from Hong Kong for trial.
MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.7% after three days of gains.
In U.S. Treasuries, the yield curve steepened after the soft inflation data pulled short-dated yields lower, indicating increased expectations among fixed income investors for a Fed rate cut.
Futures imply a roughly 80% chance of a rate cut in July and investors are looking for the Fed to give hints about a cut after their meeting scheduled for June 18-19.
Benchmark 10-year notes last rose 6/32 in price to yield 2.1205%, from 2.14% late on Tuesday.
In currency markets, Trump alarmed investors by tweeting that the euro and other currencies were "devalued" against the dollar, putting the United States at a "big disadvantage."
The dollar index, tracking the currency against six major peers, rose 0.03%, with the euro down 0.06% at $1.1322.
Oil prices fell more than 2% on Wednesday, weighed by an unexpected rise in U.S. crude inventories and a weaker demand outlook.
Hedge fund managers have been liquidating bullish oil positions at the fastest rate since late 2018 amid growing economic fears.
U.S. crude fell 2.5% to $51.94 per barrel.
Additional reporting by Aparjita Saxena in Bengaluru, Kate Duguid and Karen Brettell in New York, Marc Jones in London, Wayne Cole in Sydney; Editing by Bernadette Baum